Apparatus and methods for the acoustic inspection of a fluid conduit

Abstract

An apparatus for acoustic inspection of a fluid conduit comprises: a robot configured to move through a fluid conduit; a speaker on the robot configured to emit an acoustic excitation signal; an acoustic sensor array on the robot configured to receive reflections of the acoustic excitation signal from the conduit as the robot is moving through the fluid conduit; and a processor, configured to determine the location of an artefact in the fluid conduit from the detected reflections of the emitted acoustic excitation signal. A method comprises: positioning the robot in the conduit, emitting acoustic signals from the speaker, detecting at the sensor array reflections of the signal as the robot is moved through the conduit, and determining the location of an artefact in the conduit from the detected reflections of the emitted acoustic signal.

Description

TECHNICAL FIELD The present disclosure relates to artefact detection and localization in constrained environments. In particular, but not exclusively, it relates to an apparatus and method for the acoustic inspection of a fluid conduit. Aspects of the invention relate to an apparatus for the acoustic inspection of a fluid conduit and a method of acoustically inspecting a fluid conduit. BACKGROUND Underground infrastructure, in particular pipelines for transporting fluids such as water, oil and gas, is essential for providing products to consumers and industry. Due to increasingly aged underground infrastructure and the increasing burden on such underground infrastructure from population growth, increasing energy consumption, and climate change, there is a requirement for quicker and more reliable techniques for monitoring the condition of such underground infrastructure. Traditional robotic sensing systems working in buried pipes for condition monitoring and fault detection include closed-circuit television-based monitoring systems, but recent advances in acoustic and ultrasonic sensing techniques have offered the opportunity for improved blockage detection and condition assessment in pipes, such as sewage pipes, due to their increased detection range, reduced power consumption and reduced computation cost compared with the closed-circuit television-based monitoring systems. Acoustically reflective artefacts including blockages can be localized remotely with respect to the position of the robot using the time delay of acoustic echoes measured with an acoustic sensor from a static robot location, and such robots can be moved to new positions to aid in the determination of the direction of the echo arrival. It is an aim of the present invention to address at least some of the disadvantages associated with the prior art. SUMMARY OF THE INVENTION Aspects and embodiments of the invention provide an apparatus for the acoustic inspection of a fluid conduit, and a method of acoustically inspecting a fluid conduit, as claimed in the appended claims. According to an aspect of the invention there is provided an apparatus for the acoustic inspection of a fluid conduit, the apparatus comprising: a robot configured to move through a fluid conduit; a speaker mounted on the robot and configured to emit an acoustic excitation signal; an acoustic sensor array mounted on the robot and configured to receive reflections of the acoustic excitation signal from the fluid conduit, wherein the acoustic sensor array is configured to receive the reflections of the emitted acoustic excitation signal from the fluid conduit as the robot is moving through the fluid conduit; and a processor, configured to determine the location of an artefact in the fluid conduit from the detected reflections of the emitted acoustic excitation signal. An advantage of this invention is that improved detection and localization of one or more artefacts or objects within the fluid conduit can be provided, in particular by providing improved directional detection of artefacts or objects and improved separation of reflections from closely spaced artefacts. Further, the invention may provide a more efficient remote sensing arrangement that requires less computation and energy consumption than vision-based sensors. The robot may be an autonomous robot, such as a mobile autonomous robot. The acoustic excitation signal emitted from the speaker may sweep a predetermined range of frequencies over a predetermined measurement time period. The predetermined range of frequencies corresponds to a range of acoustic wavelengths that are larger, comparable or shorter than a characteristic dimension of the fluid conduit. The lower bound of the predetermined range of frequencies may be at a frequency that corresponds to an acoustic wavelength much larger than the characteristic dimension of the fluid conduit. The lower bound of the predetermined range of frequencies may be between 50Hz and 500Hz. The lower bound of the predetermined range of frequencies may be determined by the ability to excite sound waves with amplitudes well above the background noise level, e.g. 100Hz. The upper bound of the predetermined range of frequencies may be at a frequency that corresponds to an acoustic wavelength much shorter than the characteristic dimension of the fluid conduit. The upper bound of the predetermined range of frequencies may be 350 / 7? (Hz) in an air-filled fluid conduit, where R is the radius of the fluid conduit in meters. The upper bound of the predetermined range of frequencies may be between 2kHz and 10 kHz. The acoustic sensor array may be configured to receive the acoustic excitation signal after being reflected by artefacts in the fluid conduit. The fluid conduit may comprise a pipe. The artefacts may comprise cracks, perforations, lateral connections, joints, or blockages in the fluid conduit. The acoustic sensor array may be a circular acoustic sensor array. The acoustic sensor array may comprise one or more microphones, hydrophones, acoustic velocity receivers or accelerometers. The apparatus may comprise a velocity sensor to determine the velocity of the robot as it traverses the fluid conduit. The processor may be configured to determine the change in position of the robot from the velocity of the robot, determined by the velocity sensor, over a predetermined measurement time period. The processor may be configured to remove the effect of the robot’s body on the detected acoustic excitation signal. According to an aspect of the invention there is provided a method of acoustically inspecting a fluid conduit using the apparatus as set out above, the method comprising: positioning the apparatus in a fluid conduit; emitting an acoustic excitation signal from the speaker; detecting, at the acoustic sensor array, reflections of the emitted acoustic excitation signal as the robot is moving through the fluid conduit; and determining the location of, and direction to, an artefact in the fluid conduit from the detected reflections of the emitted acoustic excitation signal. Within the scope of this application, it is expressly intended that the various aspects, embodiments, examples and alternatives set out in the preceding paragraphs, in the claims and / or in the following description and drawings, and in particular the individual features thereof, may be taken independently or in any combination. That is, all embodiments and / or features of any embodiment can be combined in any way and / or combination, unless such features are incompatible. The applicant reserves the right to change any originally filed claim or file any new claim accordingly, including the right to amend any originally filed claim to depend from and / or incorporate any feature of any other claim although not originally claimed in that manner. BRIEF DESCRIPTION OF THE DRAWINGS One or more embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which: Figure 1 is a system diagram of an apparatus according to an embodiment of the invention; Figure 2 illustrates a perspective view of a fluid conduit, in the form of a pipe or duct in which the apparatus traverses, according to an embodiment of the invention; Figure 3 illustrates the behaviour of the first four modal shapes in a cylindrical pipe or duct; Figure 4 illustrates the position of an acoustic sensor array for plane wave reconstruction above a first cut-off frequency, as part of the apparatus according to an embodiment of the invention; Figure 5 illustrates an apparatus according to an embodiment of the invention located within a linear pipe; and Figure 6 is a flow diagram of a method of acoustically inspecting a fluid conduit using the apparatus according to an embodiment of the invention. In the drawings, like parts are denoted by like reference numerals. DETAILED DESCRIPTION Examples of the present disclosure relate to an apparatus for the acoustic inspection of a constrained environment such as a fluid conduit. In particular, examples of the present disclosure relate to an apparatus, which may be a mobile apparatus, for the acoustic inspection of a fluid conduit, capable of detecting and localizing artefacts and / or objects, such as blockages, cracks, lateral connections, joints, and junctions, within a fluid conduit, such as a pipe or duct. Non-limiting examples will now be described with reference to the accompanying drawings. It will be understood that the following examples relate to acoustic inspection of a fluid conduit, such as a pipe or duct, but may equally be applied to other constrained environments, such as fluid tanks. In particular, examples of the present disclosure provide apparatus for the acoustic inspection of a fluid conduit, such as a pipe or duct, forming, or as part of, a mobile robotic sensor system. The acoustic inspection of the fluid conduit is carried out using a frequency domain algorithm enabling the apparatus to measure the acoustic response of the fluid conduit whilst the robot is moving, that is, without stopping. Therefore, during measurement of the fluid conduit, the robot may be considered to be continuously moving. However, it may be possible that during some measurement phases the robot can take measurements with the robot static, and in between measurements the robot may be static or moving. As will be described more fully below, in relation to the accompanying drawings, this is achieved with an acoustic sensor array with algorithmic compensation of the phase shift induced by the movement of the robot. Different from a time domain algorithm with deconvolution directly applied to estimate the impulse response for robotic localization, the frequency domain method of the present disclosure compensates for the robot’s velocity and also significantly improves the precision of localization and separation of overlapped acoustic echoes coming from the opposite directions in the conduit. The figures illustrate an apparatus 10 for the acoustic inspection of a fluid conduit 100, and a method 300 of acoustically inspecting a fluid conduit 100, in particular using the apparatus 10 for the acoustic inspection of a fluid conduit 100. Figure 1 illustrates an apparatus 10 for the acoustic inspection of a fluid conduit 100 comprising a robot 20, a speaker 40, an acoustic sensor array 60, and a processor 80. The robot 20 may be any mobile platform which is able to move in a continuous manner during operation of the apparatus 10. The robot may be a tracked or wheeled vehicle, or may have any other propulsion system for traversing a fluid such as oil or water. The speaker 40, which may alternatively be called a loudspeaker, is mounted on the robot 20 in a fixed position, and is configured to emit an acoustic signal, which may be in the form of an acoustic excitation signal, which can be reflected from artefacts and objects in the fluid conduit 100. The acoustic excitation signal, also known as an excitation signal, may emit a predetermined range of frequencies over a predetermined measurement time period. The predetermined range of frequencies may be varied over time. In one example, a pseudorandom variation of frequencies may be emitted during the predetermined measurement time period. In another example, a range of frequencies may be swept during the predetermined measurement time period. Such a sweep of frequencies may be a linear sweep, sinusoidal sweep, or some other known variation of frequencies. In one example sweeping frequencies in a chirp provides an acoustic excitation signal in which frequency increases or decreases with time. Such a predetermined range of frequencies in the acoustic excitation signal provides a level of noise immunity for the apparatus 10. The predetermined range of frequencies may correspond to a range of acoustic wavelengths larger or shorter than a characteristic dimension of the fluid conduit, such as the fluid conduit size or radius. In some embodiments, the lower bound of the predetermined range of frequencies is between 50Hz and 500Hz and the upper bound of the predetermined range of frequencies is between 2kHz and 10 kHz, though it will be understood that this depends on the medium through which the apparatus 10 is travelling, the size of the fluid conduit 100 and other physical factors. In one example the lower bound of the predetermined range of frequencies is 100Hz and the upper bound of the predetermined range of frequencies is 5kHz. In other examples, in an airfilled fluid conduit, the upper bound of the predetermined range of frequencies is 350 / R (Hz). The length of the acoustic excitation signal and its frequency composition affect the signal to noise ratio, and so these parameters are chosen such that the signal to noise ratio for a particular application of the apparatus 10 is sufficiently high to accurately receive reflections from artefacts and / or objects in the fluid conduit 100. The acoustic sensor array 60 is mounted on the robot 20 in a fixed position, such that the speaker 40 and the acoustic sensor array 60 are fixed in position relative to each other. The acoustic sensor array 60 may be comprised of one or more microphones, hydrophones, acoustic velocity receivers or accelerometers. The acoustic sensor array 60 is configured to receive reflections of the acoustic excitation signal emitted from the speaker 40, in particular when reflected from artefacts and / or objects in the fluid conduit 100. The speaker 40 and the acoustic sensor array 60 are configured to operate during the movement of the robot 20. That is, the speaker 40 is configured to emit an acoustic excitation signal as the robot 20 is moving through the fluid conduit 100 and the acoustic sensor array 60 is configured to receive the reflections of the acoustic excitation signal from the fluid conduit 100 as the robot 20 is moving through the fluid conduit 100. Where the apparatus 10 may be prone to error in moving at a fixed, predetermined velocity, the apparatus 10 may comprise a velocity sensor 90, configured to determine the velocity of the robot 20 as it moves or traverses the fluid conduit 100. The velocity sensor 90 may include, for example, devices to measure rotation speed of a driveshaft, such as a shaft encoder, when applied to wheeled or tracked robots, or any other apparatus and algorithms for moving robot localization in a conduit. In other embodiments, a constant predetermined velocity over a fixed measurement distance may be assumed. Either a predetermined velocity value or a measured 7 velocity value can be fed into the algorithms of the apparatus 10 in order to compensate for the velocity of the robot 20 during operation of the apparatus 10. The processor 80 is configured to determine the location of an artefact in the fluid conduit 100 from the detected reflections of the acoustic excitation signal. The determination of the location of the artefact may include determination of a distance to the artefact and / or determination of a direction to the artefact. The processor 80 may be configured to determine the change in position of the robot 20 from the velocity of the robot 20, determined by a velocity sensor, over a predetermined measurement time period. The processor 80 may also be configured to output a control signal to the speaker, optionally via power amplification, in order for the speaker to emit the desired acoustic excitation signal. Further electronics on board the apparatus 10 may include an analog to digital converter and a digital to analog converter for handling the incoming and outgoing acoustic excitation signals. The fluid conduit 100 may comprise a pipe 100 or duct 100, through which the robot 20 traverses, moves or travels. Embodiments will be described below, generally in relation to arrangements where the fluid conduit 100 is a pipe 100, though it will be understood that the fluid conduit 100 may be a different form of environment to be measured or monitored. Figure 2 illustrates the system of coordinates in a cylindrical pipe 100 through which the apparatus 10 may move or traverse. In particular, the apparatus 10 is configured to move along the length of the cylindrical pipe 100 along an axis z. In a cylindrical pipe 100 environment the acoustic field is strongly multimodal. In the frequency domain the acoustic field in a rigid cylindrical pipe can be expressed as the superposition of modes as expressed below in Equation 1. p(r, e,z, co) = £Amn<pmn(r, 0)e^z Equation 1 where co is the angular frequency, m and n are the mode indices, <pmn is the mode shape function of a duct cross-section, Amn is the modal amplitude. The acoustic field p can be expressed in terms of acoustic pressure or any of the three acoustic velocity vector components. For an acoustically rigid wall cylindrical pipe 100 with the radius R the mode shape function is given by Equation 2 below. cos(m0)Equation 2 where denotes the mth Bessel function. If the wall of the pipe is not acoustically rigid, these functions can be predicted numerically. For example, finite element methods can be used to predict the mode shape functions in non-acoustically rigid wall cylindrical pipes, such as plastic pipes. If the pipe 100 is dry and its walls are acoustically rigid, then the wavenumber kmn in Equation 2 can be obtained from the zero-velocity condition on the rigid wall of the pipe 100, as shown in Equation 3 below. r=R 0 Equation 3 In Equation 3, ' denotes partial derivative with respect to r. The z-axis wavenumber in Equation 1 is given by Equation 4 below. Ymn = Equation 4 where ko is the wavenumber in a free space (k0 = <y / c0, Co is sound speed in air and w is the angular frequency). If the pipe is not dry and its walls are not acoustically rigid, then the above quantities are predicted numerically. For example, finite element methods can be used to predict the wavenumbers in non-acoustically rigid wall cylindrical pipes, such as plastic pipes. Equation 4 therefore predicts the wavenumber at which acoustic modes at different frequencies propagate in the pipe 100. It is clear that ymn is frequency dependent, i.e., the acoustic propagation of these modes (except in the case of plane wave when k00 = 0) is dispersive. When the free field wavenumber ko is larger than the eigen-number kmn, or the frequency is above the corresponding eigen-frequency, fmn = kmnc0 / (2n), a particular acoustic mode can propagate along the pipe 100 with relatively little attenuation at a phase velocity that is dispersive. Figure 3 shows schematically the angular and radial dependence of the first four mode shapes in a cylindrical pipe 100. In Figure 3 the plus or minus signs correspond to the sign that the mode shape, <pmn, takes for a given values of 6 and r in Equation 1. In some embodiments the acoustic sensor array 60 is a circular acoustic sensor array 60. The acoustic sensor array 60 may allow selection of a particular part of the sound-field useful for the detection of artefacts or objects in the pipe 100, or of a particular artefact or object, such as a crack or blockage, in the pipe 100. In some embodiments several acoustic sensors may be arranged circumferentially in the circular acoustic sensor array 60. In some examples four, five, six, seven, eight, nine, or ten acoustic sensors may be arranged in the acoustic sensor array 60. In some embodiments a greater number of acoustic sensors may be used, though with an impact on the cost of the apparatus. In the example of Figure 4, six acoustic sensors comprise the acoustic sensor array 60. The acoustic sensor array 60 may be circumferentially arranged on the robot 20, such that, in use, the acoustic sensor array 60 is circumferentially arranged relative to the pipe 100 through which the robot 20 traverses. The robot 20 can then move linearly along the length of the pipe 100 with each of the acoustic sensors being retained at substantially a constant distance from the inner surface of the pipe 100. Such a circular acoustic sensor array 60 can be used to extract the plane wave mode in the frequency range well above the first cut-off frequency. Figure 4 illustrates an example position of the acoustic sensor array 60 for plane wave reconstruction above the first cut-off frequency, where the location of the microphones in the acoustic sensor array 60 are positioned circumferentially relative to the inside of the wall of the pipe 100, that is, equally, or substantially equally, spaced from the inner surface of the wall of the pipe 100. This enables the cancellation of the first two non-axisymmetric modes (1,0), (2,0) by averaging the measured acoustic response to extract the axisymmetric mode, so that only the plane wave can be obtained over a relatively broad frequency range. For example, the acoustic sensors in the acoustic sensor array 60 may be positioned the along the yR (0 <y <1) circumference enabling the mute of the axisymmetric mode (e.g. foi = 2789 Hz for a 150 mm dry pipe) and the optimal cancellation of the first two non-axisymmetric modes (1,0), (2,0) by averaging the measured acoustic response so that only the plane wave can be 10 obtained over a frequency range of 0 to 4 kHz for the 150mm pipe. Different diameter pipes, different pipe materials, and different media within the pipe 100, may require different positioning of the acoustic sensors in the acoustic sensor array 60, as will be understood by the skilled person, e.g. with 0.6 <y <0.7. In various examples described herein, such a circular acoustic sensor array 60 is provided, where only the plane wave is extracted from the multi-modal acoustic field and analysed, for example, in the frequency range of up to k0R <6.5. For an acoustic sensing system with the static excitation and receiver points collocated in the pipe 100, the acoustic response at the plane wave mode (ymn = k0 in Equation 1) can be expressed as in Equation 5 below. = Xq^Aoo^e-^^-^Sq^Zq) + n(,0)) Equation 5 where z0 is the coordinate of the robot 20, zq is the discrete axial coordinates, zQ is the maximum measurement distance determined by the duration of the acquired signal. The resolution of the coordinates, zq, is dependent on the time resolution when sampling of the reflected acoustic excitation signal because zq = cotq, where tq is the qth time sampling interval. Sq(zq) is the amplitude of the reflection from the artefact located at the position zq. When there are no artefacts at zq, sq(zq) is equal to zero. It is expected that the amplitudes of the acoustic waves reflected from the artefacts s (with elements sq) is a sparse vector (which has many zeroes) due to the sparse nature of the artefacts in a pipe network. 400(w) is the spectrum of the excitation signal in the plane wave mode, that is the acoustic excitation signal emitted from or by the speaker 40 (which may be a chirp, where the acoustic excitation signal increases or decreases in frequency over time, that is, the acoustic excitation signal emitted from or by the speaker 40 sweeps a predetermined range of frequencies over a predetermined measurement time period), -n(w) denotes the noise signal present in the pipe or electronics. Note that the phase lag term in the exponent e-2iko\zq-zo\ uses twice the distance between the apparatus 10 and the artefacts because the wave propagates from the apparatus 10 to the artefacts and reflected back. As the acoustic sensing system is mounted on a moving robot 20, the phase lag due to the moving robot 20 is compensated for. In some conduits such as pipes, the pipe ends 102, 104 may have rigid terminations or connected to a larger manhole which may be present at the front and / or rear of the apparatus 10 as shown in Figure 5. These may cause the reflections of the emitted acoustic wave. Therefore, the wavenumber in Equation 5 can take either the positive or negative sign depending upon the direction with respect to the position of the apparatus 10. The proposed invention makes it possible to identify the direction of the received acoustic echoes from the artefacts with respect to the sign of the velocity at which the robot 20 is moving. Assuming that zo=O, s can be written as a vector of positive or negative coordinates. For an artefact at a negative coordinate behind the robot 20, the reflected acoustic wave propagates in the positive direction so that the wavenumber in Equation 5 is positive. For an artefact located in the positive direction in front of the robot 20, the wavenumber should be negative. As observed in Equation 5, it is the difference between the positions of the moving robot 20, z0, and artefact, zq, which is of importance rather than their absolute coordinates. In this way the phase compensation to account for the moving robot 20 can be written as below in Equation 6. = ^Qq=-QA00^e~2i\k°z<i\-^^ Equation 6 where vr is the velocity of the robot 20, signQ) is the signum function, tr is the time lag of the excitation. If a linear chirp (sinusoidal sweep) signal is used as the excitation, then the time lag from the robot 20 can be expressed as shown below in Equation 7. tr (6j) = T(w — 6)1) / (6)2 — <^i) Equation 7 where and 6)2 are the instantaneous frequency at the beginning and end of the chirp, respectively, and T is the duration time of the chirp. An alternative excitation signal can be used to achieve a similar algorithm efficiency as long as it delivers enough acoustic energy across the specified frequency range. In this case the equation for tr(6)) is more complicated. Again, the velocity for the phase compensation term (e~2sign(^q)[ikovrt^^ iS Of the robot velocity vr, due to the doubled distance of wave propagation between the robot 20 and the artefacts. Note that the acoustic excitation emitted from the moving robot 20 is also presented in Equation 6 by terms A00(o)) and sq(zq), where the former corresponds to the spectral amplitude, and the latter corresponds to the spatial amplitude. The spatial amplitude of acoustic excitation covers twice the distance of the moving robot 20 with T chirp duration, due to the twice of the robot velocity vr used for the phase compensation. In order to estimate the location of the artefacts, Equation 6 can be solved as an acoustic inverse problem, which can be written as matrices in the discrete frequency domain as in Equation 8 below. ^1,-Q ^2,-Q h-L-Q hi,i—Q ^2,1-Q h-L.l-Q Equation 8 where hlq = A00(lAf)e-2qk(>([Af)q^ Af is frequency domain resolution of the discrete Fourier transform used to calculate the acoustic response spectrum in Equation 1, At is the temporal resolution of the time series recorded on the array of acoustic receivers, I, q are the indices of the frequency and distance points, respectively, L and 2Q are the total numbers of the frequency and distance points, respectively. When L is larger than 2Q, the inverse problem of Equation 8 is over-determined and can be solved using the Least Square (LS) method, e.g. the standard LS method with QR factorization or another suitable method applied for over-determined systems of equations. In a particular case for a static robot 20, the elements of the transfer matrix htq are equal to hi-q. The estimated artifacts amplitude sq is also equal to s_q. Hence, Equation 8 with 2Q can be reduced to a smaller dimension and rewritten as Equation 9 below. ^1,0 ^1,1 ^2,0 ^2,1 ^1,0 ^L,l Equation 9 where hlq = A00(lAf)e 2i\koq^f)qco^t\. However, the direction of the acoustic echo from an artefact is impossible to determine using the Fourier transform of the time series for the acoustic response recorded on a static robot 20 because of the missing term -2sj^n(q)[j / c0(ZAf)vrtr(ZAf)] in Equation 9. Therefore, only the positive coordinates toward the artefact can be used in this limiting case. In embodiments of the present disclosure, the direction of the acoustic echo from an artefact or object is determinable since the apparatus 10 is moving and is not static during the emission of the acoustic excitation signal or reception of the reflections of the acoustic excitation signal from the fluid conduit 100. Bayesian learning may be used for the over-determined linear inverse problem in Equation 8 and Equation 9. The positions of artefacts and objects can be determined by Bayesian estimation, in particular by using estimators such as maximum likelihood (ML) or maximum a posteriori (MAP). In a first Bayesian estimation method, using maximum likelihood, the probability density function J’ of the artefact’s amplitude vector s given an observation for the acoustic response p can be described as below in Equation 10. (s|p) = Equation 10 JpyP) The likelihood of the signal p given the artefacts amplitude vector s is the probability density function of the random noise is as given below in Equation 11. ?P\s(p\s) = = ^(p-hs) Equation 11 Assuming that n is random noise with a Gaussian distribution and the mean, pn, and constant covariance on, then the likelihood function is as given below in Equation 12. Pp\s(p\s) =——rexp [-^ (p-hs-p^tp - hs - pn) Equation 12 (271^)2 where H denotes the conjugate transpose. The estimated artefact’s location is obtained from the maximization of the log-likelihood function, In^^CpIs)], with respect to sand given by Equation 13 below. hHhs = hH(p - [in) Equation 13 When hHh is well-posed, Equation 13 is replaced with Equation 14 below. s = (hHh) 1hH(p — [tn) Equation 14 If [in = 0 the additive background noise is white Gaussian noise with zero-mean value, Equation 14 is then equivalent to the previously noted least squares solution. Alternatively, in a second Bayesian estimation method, the maximum a posterior estimate sMAP is obtained as the artefacts amplitude vector that maximises the posterior probability density function, as shown in Equation 15 below. arg max , . . arg max ?v\s(p\s)?s(s) Smap= \ ?s\p(s\p)= % Equation 15 Assuming that the mean noise is zero [in = 0, and the estimated artefacts s is a multivariate generalised Gaussian distribution as below in Equation 16. Ps(s) oc exp ||s||“l Equation 16 where Ss is the covariance of vector s, a is the norm type parameter. The posterior distribution can be obtained by substituting Equation 12 into Equation 15, to obtain Equation 17 below. ?s\P(s\p) = 77T—--r—-exp [-A(p - hs)H(p - hs) - Equation 17 ^^(271^)2(271)21^12 L 2 J The maximum a posterior estimation of the artefacts can then be obtained by differentiating the log-posterior probability density function, In and setting the derivative to zero. The maximum a posterior estimate is given by Equation 18 below. Smap = arg™n [jll / is -p^ + A||s||“] Equation 18 where A is known as the regularization parameter A = and ^-norm penalty function is given by ||s||“ = It is assumed that the acoustic artefacts have a limited spatial extent, so that the vector s has sufficient sparsity. The sparse nature of the artefacts (e.g. blockages / junctions) is common in drainage pipes 100. It is known that the sparsity of impulse response in the pipe 100 can be observed in the time domain and wavelet domain. The sparse representation using wavelet basis functions can reduce the background noise and some high order modal components in the impulse response, without cancelling the acoustic features from artefacts. The most intuitive sparsity for the penalty function ||s||“ is / b-norm regularization. When a = 0, the penalty function is formally called / b-norm, the number of non-zero components of the vector. Therefore, minimizing the penalty function ||s||0 means minimizing the number of nonzero components of vector s, which leads to a non-convex and non-smooth optimization problem for Equation 18. Fortunately, it is possible to relax the optimization in Equation 18 to a convex / i-minimization for the convenience to solve it. When a =1, it is called the / i-norm regularization, which describes the sum of absolute values of the elements of p. The / i-norm is usually used to induce sparsity in the optimal solution of Equation 18. The / i-norm regularization may be solved using the Sparse Reconstruction by Separable Approximation algorithm (SpaRSA) or another suitable regularization algorithm. After estimating the amplitude vector s, the location of the artefacts can be obtained directly from the non-zero components sq associated to its axial coordinates zq. A technique of the present disclosure for the localization of artefacts in the pipe 100 with mobile sensor array compensation is defined in Table 1 below. Table 1 presents the maximum likelihood method with compensation for the mobile robot 20 with the acoustic sensor array 60. Task: To estimate the location of artefacts in the pipe § Input: Excitation chirp signal c(f), Response signal from M acoustic sensors pm(t) m=1:M Plane wave reconstruction: p(t) = E^iPmCO Fast Fourier transform: pC^) = TTT(p(tj}, Aoo(«)) = Transfer matrix: h^Zq) = ML solution: §= (hHh) 'h"p Output: § Table 1. Algorithm 1 - frequency domain maximum likelihood with mobile compensation. A technique of the present disclosure for the localization of artefacts in the pipe 100 with mobile 5 compensation using / i-norm regularization maximum a posterior is summarized in Table 2. Task: To estimate the location of artefacts in the pipe § Input: Excitation chirp signal Aoo (f), response signal from M acoustic sensors pm(t) m=1:M Plane wave reconstruction: p(t) = E^iPmCO Fast Fourier transform: pCw) = TTT{p(t)}, A00(oj) = ??T{A00(t)} Transfer matrix: h(<A),zq) = AOo(")e_2‘lfeo^Zqi_2s‘5"(Zq)i‘feo^ Initialization: k=1, A = h, xr = p, = ATA, tolerance e = 10-5, parameter A = 0.001 Iteration: 1. Ak = max{0.1||ATxk||oo,A} 2. Exploit soft shrinkage: sk+1 = shrink(sk — AT(Ask — x) / Tk,Ak / Tk ) (where shrink(si,A) = signCsJ maxflsj — A, 0}) ........................................................................ o. upuaie u le aiep ik (Sfc+1-Sfc)T(sfc+1_Sfc) 4. If <Ei go to step 5. Otherwise, return to step 2 sk 5. sk+i = x — Ask+1 6. If Ak <A, stop; Otherwise k=k+1, and return to step 1. Output: s = sk Table 2. Algorithm 2 - frequency domain maximum a posterior estimation with / i-norm regularization with SpaRSA to localize artefacts in a pipe. Figure 6 illustrates a flow diagram of a method 300 of acoustically inspecting a fluid conduit 100 such as a pipe 100, in particular for detecting artifacts and / or objects in the fluid conduit 100 using an apparatus 10 for the acoustic inspection of a fluid conduit 100. In particular, the method 300 of acoustically inspecting a fluid conduit 100 can be carried out using the apparatus 10 as previously described. Some blocks of the method 300 may be carried out using processing means, such as a processor 80 or processing circuitry integral with, or operably connected to, the apparatus 10. The method 300 comprises block 302 where the apparatus 10 is positioned in a fluid conduit 100, such as a pipe 100 or duct 100. At block 304 the method 300 comprises: emitting an acoustic excitation signal from the speaker 40. Acoustic excitation signals, for example signals with a pseudo-random frequency variation or chirps, which last for longer periods of time, such that measurements taken by the acoustic sensor array 60 are made over longer temporal measurement periods, provide for improved detection and localization of artefacts and / or objects as more data points are collected during the measurement period. In some examples, acoustic excitation signal duration may be between 1 second and 60 seconds. For example, an acoustic excitation signal period of 10 seconds or 20 seconds may be used, whilst the robot 20 travels through the fluid conduit 100. At block 306 reflections of the acoustic excitation signal are detected, at the acoustic sensor array 60, as the robot 20 is moving through the fluid conduit 100. Optionally, at block 308 velocity information relating to the velocity of the robot 20 as the robot 20 is moving through the fluid conduit 100 is determined by a velocity sensor 90 on the apparatus 10. At block 310 the location of an artefact or object, or a plurality of artefacts and / or objects in the fluid conduit 100 is determined from the detected reflections of the acoustic excitation signal with a Bayesian estimate or similar maximum likelihood algorithm. Optionally, at block 312 data relating to the location of artefacts and objects may be output from the apparatus 10 to an observer or a data recorder system external to the apparatus 10. The data may be sent through a wired connection when using a tethered robot 20, or wirelessly if the robot 20 is wirelessly connected. Data can also be saved and stored in the robot memory card (e.g. a secure digital (SD) card) to be subsequently used for post-processing. In some embodiments, the movement of the robot 20 during data acquisition may cause the presence of a blind zone for the localization algorithms. In order to minimize the effect of blind zones on data acquisition, two or more consecutive measurements may be taken whilst the robot moves first forwards and then backwards over the same distance. The two or more measurements may then be fused to produce a single data measurement set which minimizes or negates the blind zone. Alternatively, the robot’s acoustic signature can be measured or calculated to be then compensated for by subtracting it from the signal recorded on the acoustic sensor array 60. Although embodiments of the present invention have been described in the preceding paragraphs with reference to various examples, it should be appreciated that modifications to the examples given can be made without departing from the scope of the invention as claimed. The apparatus 10 for the acoustic inspection of a fluid conduit 100 and methods 300 described herein can be adapted for use with different applications and to detect different artefacts and / or objects. The apparatus 10 for the acoustic inspection of a fluid conduit 100 and methods 300 described herein can be used, for example, in applications such as autonomous mobile robot dry pipe inspection or tethered mobile robot dry pipe inspection, such as gas pipe inspection, but can equally be used in wet pipe applications, such as water supply inspection, or in partially wet and partially dry pipe applications such as waste water pipe inspection. The pipe 100 may be, for example, a wastewater pipe, a sewer pipe, a water supply pipe, a gas pipe, an oil pipe, an air duct, or any other pipe or duct in which sound, emitted by the speaker 40, can travel and reflect from artefacts within the pipe 100 or duct 100. Of course, the apparatus 10 for the acoustic inspection of a fluid conduit 100 and methods 300 described herein are not to be limited to such applications. Features described in the preceding description may be used in combinations other than the combinations explicitly described. 5 Although functions have been described with reference to certain features, those functions may be performable by other features whether described or not. Although features have been described with reference to certain embodiments, those features may also be present in other embodiments whether described or not. 10 Whilst endeavoring in the foregoing specification to draw attention to those features of the invention believed to be of particular importance it should be understood that the Applicant claims protection in respect of any patentable feature or combination of features hereinbefore referred to and / or shown in the drawings whether or not particular emphasis has been placed 15 thereon.

Claims

1. An apparatus for the acoustic inspection of a fluid conduit, the apparatus comprising:a robot configured to move through a fluid conduit;a speaker mounted on the robot and configured to emit an acoustic excitation signal as the robot is moving through the fluid conduit;an acoustic sensor array mounted on the robot and configured to receive reflections of the acoustic excitation signal from the fluid conduit, wherein the acoustic sensor array is configured to receive the reflections of the emitted acoustic excitation signal from the fluid conduit as the robot is moving through the fluid conduit;a velocity sensor to determine the velocity of the robot as it traverses the fluid conduit’ and;a processor and at least one algorithm configured to process velocity sensor data and acoustic sensor data received as the robot is moving through the fluid conduit involving phase compensation for movement of the robot through the fluid conduit based on a difference between the data received by the moving robot at different positions within the fluid conduit and, to determine the location of an artefact in the fluid conduit.

2. An apparatus according to claim 1, wherein the robot is a mobile autonomous robot.

3. An apparatus according to any preceding claim, wherein the acoustic excitation signalemitted from the speaker sweeps a predetermined range of frequencies over a predetermined measurement time period.

4. An apparatus according to claim 3, wherein the lower bound of the predetermined range of frequencies is between 50Hz and 500Hz.

5. An apparatus according to claim 3 or claim 4, wherein the lower bound of the predetermined range of frequencies is 100Hz.

6. An apparatus according to claim 3, wherein the upper bound of the predetermined range of frequencies is 350 / R (Hz) in an air-filled fluid conduit, where R is the radius of the fluid conduit in meters.

7. An apparatus according to claim 3 or claim 6, wherein the upper bound of the predetermined range of frequencies is between 2kHz and 10 kHz.

8. An apparatus according to any preceding claim, wherein the acoustic sensor array is configured to receive the acoustic excitation signal after being reflected by artefacts in the fluid conduit.

9. An apparatus according to claim 8, wherein the fluid conduit comprises a pipe.

10. An apparatus according to claim 8 or claim 9, wherein the artefacts comprise cracks,perforations, lateral connections, joints, or blockages in the fluid conduit.

11. An apparatus according to any preceding claim, wherein the acoustic sensor array is a circular acoustic sensor array.

12. An apparatus according to any preceding claim, wherein the acoustic sensor array comprises one or more microphones, hydrophones, acoustic velocity receivers or accelerometers.

13. An apparatus according to any preceding claim, wherein the processor is configured to:determine the change in position of the robot from the velocity of the robot, determined by the velocity sensor, over a predetermined measurement time period.

14. An apparatus according to any preceding claim, wherein the processor is configured to:determine the direction to an artefact in the fluid conduit from the detected reflections of the emitted acoustic excitation signal.

15. An apparatus according to any preceding claim, wherein the processor is configured to:remove the effect of the robot’s body on the detected acoustic excitation signal.

16. A method of acoustically inspecting a fluid conduit using the apparatus as claimed in any of claims 1 to 15, the method comprising:positioning the apparatus in a fluid conduit;emitting an acoustic excitation signal from the speaker;detecting, at the acoustic sensor array, reflections of the emitted acoustic excitation signal as the robot is moving through the fluid conduit;determining the velocity of the robot as it traverses the fluid conduit using a velocity sensor; andprocessing velocity sensor data and acoustic sensor data received as the robot is moving through the fluid conduit involving phase compensation for movement of the robot through the fluid conduit based on a difference between the data received by the moving robot at different positions within the fluid conduit and;determining the location of an artefact in the fluid conduit based on the step of processing velocity sensor data and acoustic sensor data.

17. A method according to claim 16, the method comprising:determining the direction to an artefact in the fluid conduit from the detected reflections of the emitted acoustic excitation signal.

18. A method according to claim 15 or claim 17, the method comprising:removing the effect of the robot’s body on the received reflections of the emitted acoustic excitation signal.

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