Method and system for characterizing an elongated medium

Abstract

Methods and systems for diagnosing the structural condition of an elongated medium using a vibration generator and a sensing unit coupled to medium are disclosed. The methods include generating of a vibro-acoustic signal to propagate into the medium from an input location along the medium, with a frequency band to excite a single mode of vibration of the medium. The frequency band overlaps at least a resonant frequency of the single mode of vibration. There is a measuring at an output location along the medium, of a response signal representative of a dynamic response of the medium to the vibro- acoustic signal, a computing the dynamic response, and a tracking of variation of the resonant frequency of the single mode of vibration between the input location and the output location.

Description

METHOD AND SYSTEM FOR CHARACTERIZING AN ELONGATED MEDIUM CROSS-REFERENCE TO RELATED APPLICATION

[0001] The present application claims the priority of United Stated Patent Application Serial No. 63 / 746,117, filed on January 16, 2025, the entire content of which is incorporated herein by reference.FIELD

[0002] The application generally relates to the field of dynamic characterization methods, and more precisely to the field of characterizing dynamic responses of elongated media and deriving structural properties thereof.BACKGROUND

[0003] The characterization and structural diagnostic of long structures such as road, pipelines, conduits, bridges, and so on comes with its own challenges. For instance, the characterization of segments of an aqueduct can be challenging without digging out the pipes.

[0004] In order to efficiently characterize and diagnose complex elongated structures, multiple methods have been developed to address particular problems. Time of flight monitoring of the acoustical impulse response of an initial impulse is a method that is able to pinpoint the location of defects in a structure. However, this method often lacks precision as the variation in the condition of a structure affects the measurements. Electromagnetic characterization to diagnose the condition of a structure is a method that may have a higher precision on the determination of the position of a defect as opposed to time of flight monitoring, and such method may give information on the type of defect. However, electromagnetic characterization methods are costly and not well suited to characterize complex structures composed of several non-metallic subcomponents, such as in a Prestressed Concrete Cylinder Pipe (PCCP). In addition, invasive methods to conduct structural diagnostics, such as by using robots and imaging devices inside the pipes, can be implemented, but involve costly operations.SUMMARY

[0005] In accordance with a first aspect, there is provided a method for diagnosing a structural condition of an elongated medium using a vibration generator and a sensing unit coupled to elongated medium, the method comprising: generating, via the vibrationgenerator, a vibro-acoustic signal to propagate into the elongated medium from an input location along the elongated medium, the vibro-acoustic signal has a frequency band configured to excite a single mode of vibration of a plurality of modes of vibration of the elongated medium, the frequency band overlapping with at least a resonant frequency of the single mode of vibration; measuring at an output location along the elongated medium, via the sensing unit, a response signal representative of a dynamic response of the elongated medium to the vibro-acoustic signal and transducing the response signal into an output signal; computing the dynamic response of the elongated medium from the output signal; and tracking a variation of the resonant frequency of the single mode of vibration between the input location and the output location, the variation of the resonant frequency corresponding to a variation of the structural condition of the elongated medium between the input location and the output location.

[0006] Further in accordance with the above aspect, for example, the method further comprises selecting the frequency band of the vibro-acoustic signal from first, at least: propagating a first vibro-acoustic signal into the elongated medium, the first vibro-acoustic signal configured to excite the plurality of modes of vibration of the elongated medium; measuring at the output location, via the sensing unit, a first response signal representative of a first dynamic response of the elongated medium to the first vibro-acoustic signal and transducing the first response signal into a first output signal; computing the first dynamic response of the elongated medium from the first output signal; and identifying the resonant frequency of the single mode of vibration at least from the computing of the first dynamic response.

[0007] Further in accordance with the above aspects, for example, propagating the first vibro-acoustic signal into the elongated medium includes generating the first vibro-acoustic signal via the vibration generator, the first vibro-acoustic signal having a frequency bandwidth adapted to excite the plurality of modes of vibration of the elongated medium.

[0008] Further in accordance with the above aspects, for example, the first vibro-acoustic signal includes a plurality of vibro-acoustic waves each having a frequency corresponding to a respective predetermined resonant frequency of the elongated medium.

[0009] Further in accordance with the above aspects, for example, the method further comprises determining the respective predetermined resonant frequencies of theelongated medium from a model of the elongated medium, wherein the model is an analytical and / or experimental model of the elongated medium.

[0010] Further in accordance with the above aspects, for example, the respective predetermined resonant frequencies include a predetermined fundamental resonant frequency and harmonics of the predetermined fundamental resonant frequency.

[0011] Further in accordance with the above aspects, for example, the method further comprises generating the model of the elongated medium from properties of the elongated medium.

[0012] Further in accordance with the above aspects, for example, determining the respective predetermined resonant frequencies of the elongated medium includes performing a modal analysis of the model.

[0013] Further in accordance with the above aspects, for example, the method further comprises selecting the frequency band of the vibro-acoustic signal by first: computing an analytical model of the elongated medium from properties of the elongated medium; selecting a single expected mode of vibration from a plurality of expected modes of vibration of the elongated medium obtained from the computing of the analytical model and; propagating a first vibro-acoustic signal into the elongated medium, the first vibro-acoustic signal configured to excite the single expected mode of vibration of the elongated medium, the first vibro-acoustic signal having a frequency band including at least an expected resonant frequency of the single expected mode of vibration.

[0014] Further in accordance with the above aspects, for example, tracking the variation of the resonant frequency of the single mode of vibration between the input location and the output location includes deconvoluting the dynamic response of the elongated medium.

[0015] Further in accordance with the above aspects, for example, the method further includes discretizing the deconvoluted dynamic response of the elongated medium into a plurality of time windows.

[0016] Further in accordance with the above aspects, for example, the method further comprises selecting a duration of a time window of the plurality of time windows based on a wavelength of the vibro-acoustic signal.

[0017] Further in accordance with the above aspects, for example, the method further comprises averaging a frequency bandwidth of each time window of the plurality of time windows to obtain a dynamic response value representative of a mean or average value over each time window of the plurality of time windows as a function of a position between the input location and the output location.

[0018] Further in accordance with the above aspects, for example, identifying the resonant frequency of the single mode of vibration at least from the computing of the first dynamic response includes: selecting an harmonic frequency of a mode of vibration of the plurality of modes of vibration obtained from the first dynamic response, the resonant frequency of the single mode of vibration being the harmonic frequency.

[0019] Further in accordance with the above aspects, for example, the method further comprises selecting the frequency band of the vibro-acoustic signal by first: generating, via the vibration generator, a first vibro-acoustic signal to propagate into the elongated medium from the input location along the elongated medium, the first vibro-acoustic signal having a first frequency band configured to excite a single mode of vibration of a plurality of modes of vibration of the elongated medium, the first frequency band overlapping at least a predetermined resonant frequency of the single mode of vibration; measuring at the output location along the elongated medium, via the sensing unit, a first response signal representative of a first dynamic response of the elongated medium to the first vibro-acoustic signal and transducing the first response signal into a first output signal; computing the first dynamic response of the elongated medium from the first output signal; and identifying a peak frequency value from the first dynamic response within the first frequency band, and selecting a frequency at the peak frequency value as the resonant frequency to be overlapped by the frequency band of the vibro-acoustic signal.

[0020] Further in accordance with the above aspects, for example, the method further comprises selecting the single mode of vibration from the plurality of modes of vibration of the elongated medium based on at least one of: a desired resolution of the dynamic response of the elongated medium; a desired resolution of the tracking of the variation of the resonant frequency between the input location and the output location; a desired resolution of the tracking of the variation of the structural condition of the elongated medium between the input location and the output location; or a dynamic behavior of a subcomponent of the elongated medium.

[0021] Further in accordance with the above aspects, for example, the method further comprises obtaining the predetermined resonant frequency of the elongated medium from a digital twin of the elongated medium.

[0022] Further in accordance with the above aspects, for example, the method further comprises generating the digital twin of the elongated medium from properties of the elongated medium.

[0023] Further in accordance with the above aspects, for example, the structural condition of the elongated medium is a wall thickness or wall stiffness of the elongated medium.

[0024] In accordance with a second aspect, there is provided a data acquisition system for diagnosing a structural condition of an elongated medium, comprising: a vibration generator for exciting the elongated medium with a first vibro-acoustic signal at an input location along the elongated medium; a sensing unit for measuring a response signal representative of a dynamic response of the elongated medium to the first vibro-acoustic signal of the elongated medium at an output location along the elongated medium; and a processing unit configured to execute instructions for: computing the dynamic response of the elongated medium based on an output signal from the sensing unit, the output signal transduced from the response signal measured by the sensing unit, identifying an estimated resonant frequency of a mode of vibration of the elongated medium from the computed dynamic response; and causing a generation of a second excitation signal, by the vibration generator, to propagate into the elongated medium, the second excitation signal having a frequency band including or overlapping with at least the estimated resonant frequency of the mode of vibration.

[0025] Further in accordance with the above aspect, for example, the processing unit is configured for transducing the response signal into the output signal.

[0026] Further in accordance with the above aspects, for example, the processing unit forms part of the vibration generator and / or the sensing unit.DESCRIPTION OF THE FIGURES

[0027] Fig. 1 is a schematic view of a system for characterizing an elongated medium, in accordance with one or more embodiments;

[0028] Fig. 2 is a schematic view of a sensing unit of the system of Fig. 1, in accordance with an embodiment;

[0029] Fig. 3 illustrates an embodiment of the system of Fig. 1 for characterizing an elongated medium, in accordance with an embodiment;

[0030] Fig. 4 illustrates another embodiment of the system of Fig. 1 for characterizing an elongated medium, in accordance with an embodiment;

[0031] FIGS. 5A-5C are cross-section illustrations of elongated media, in accordance with some embodiments;

[0032] Fig. 6 is a flow chart of a method for characterizing an elongated medium to assess its structural condition, according to an embodiment; and

[0033] Fig. 7 is a block diagram of an exemplary computing device of the system of Fig. 1, in accordance with an illustrative embodiment.DETAILED DESCRIPTION

[0034] The methods and systems presented herein relate to the characterization of an elongated structure using excitation on a per vibration mode basis, which enables a characterization of the dynamic response of such elongated structure for that mode independently from the dynamic response at other vibration modes the elongated structure may have. The characterization also relies on the selective tracking of a variation in frequency of a targeted vibration mode along the elongated structure. The technology presented herein also relies on the determination and use of higher harmonics of a selected mode of vibration to improve the resolution of the measurements. Thus, the recursive characterization of the elongated structure using refined signals to excite modes of vibration individually or excite a selected combination of modes of vibration may be able to provide more efficiently information on the condition (the ‘health’) of complex structures.

[0035] A system 100 for characterizing an elongated medium will first be described, for context. Referring to Fig. 1 , there is shown a schematic illustration of an embodiment of a system 100 for characterizing an elongated medium 102. In operation, the system 100 may characterize the dynamic behavior of the elongated medium 102 using vibroacoustic signal generation and measurements. The system 100 comprises a vibration generator 104 configured for generating a vibro-acoustic signal to propagate in the elongated medium 102, and a plurality of sensing units 200a, b,c operatively coupled to the elongated medium 102 at selected locations along the elongated medium 102 to sense the generated vibro-acoustic signal that is propagating therein. The sensing units 200a, b,c are communicatively coupled to a computing device 106 for processing measurementsobtained by the sensing units 200a, b,c. In at least some embodiments, the computing device 106 is in communication with a user interface 108. In at least some embodiments, the computing device 106 is in wireless communication with the sensing units 200a, b,c via a wireless network 110. The wireless network may be, for instance, the Internet, a local-area network (LAN), a personal-area network (PAN), a metropolitan-area network (MAN), a wide-area network (WAN), and the like. Wired communication between the sensing units 200a, b,c and the computing device 106 may also be contemplated. Features of the computing device 106 will be described later with respect to an exemplary computing device 700 with reference to Fig. 7.

[0036] It will be appreciated that the present technology is directed to the field of vibroacoustics, which lies at the interface of acoustics and structural dynamics. Generation, propagation and measurement of vi bro-acoustic signals may be performed in both solid and fluid media. As such, the present technology is not limited to fluids, which is generally the case for acoustic waves.

[0037] In at least some embodiments, the elongated medium 102 is composed at least partially of a material dynamically responsive to the propagation of vibro-acoustic signals, such as steel, iron, copper and / or any suited alloy. In at least some embodiments, the elongated medium 102 may include plastic such as polyvinyl chloride (PVC) as other possibilities. In at least some embodiments, the elongated medium 102 is a prestressed concrete pipe made of a concrete and optionally of steel wires configured for providing tensile stresses to the pipe. The concrete pipe may be wire-wrapped, asbestos cement or any other type of concrete pipe, e.g., prestressed concrete pressure pipe (PCCP) having a steel core cylinder with concrete layers inside and outside. It will be appreciated that various other types of material not listed herein may be subject to the present technology.

[0038] The elongated medium 102 may have various shapes depending on the application. In at least some embodiments, the elongated medium 102 has a tubular shape, which may have cylindrical cross-section or other possible cross-section such as oval, obround, square, circle, rectangular, hexagonal or other polygonal shape. The diameter (or other transverse dimensions) and wall thickness may be constant or vary along an elongation axis X. In at least some embodiments, the elongated medium 102 is configured to contain pressurized fluid therein. In at least some embodiments, the elongated medium 102 is a pipe of a pressurized network, such as a pipeline network oran aqueduct network. In other embodiments, the elongated medium 102 may be a soundpropagating section or a beam of a structure underground or above the ground surface.

[0039] The vibration generator 104 is operatively coupled to the elongated medium 102. The vibration generator 104 is configured to generate an input signal 112 in the form of a vi bro-acoustic excitation, which may be in the form of a wave or waves that, propagate in the elongated medium 102. The vibration generator 104 is an electronic device that may generate a vibro-acoustic excitation by selecting and / or controlling various properties of a wave signal, including the amplitude(s), the frequency(ies), the duration(s) and the shape thereof. In at least some embodiments, the vibration generator 104 may be portable. Compactness and weight of the vibration generator 104 may be adapted to facilitate handling by an operator. This may be particularly advantageous to transport the vibration generator 104 between test sites, with limited equipment or workforce. In some alternatives, a modal hammer may be used to excite the elongated medium 102 in addition to the vibration generator 104. As shown in Fig. 1, and as will be further described below, the vibration generator 104 may be configured for generating propagating vibro-acoustic waves 114 along the elongated medium 102. In response to the generated vibro-acoustic waves 114, the elongated medium 102 may enter in a state of resonance, thereby generating other propagating waves of various harmonics or stationary waves 114, or a combination thereof.

[0040] The generated input signal 112, which may be referred to as a generated excitation signal, may be defined by a complex function including one or more sinusoids or other waveforms of different timing, frequencies and / or amplitudes. Generally, the input signal 112 has a duration longer than the time needed to propagate through the elongated medium 102. The generated input signal 112 could also include one or more step-function. In at least some embodiments, the vibration generator 104 is configured to operate at frequencies in the range of 5 to 2000 Hz, which may be a range suited for characterizing pipes. In other embodiments, for example where the elongated medium 102 is a medium other than a pipe, the frequency range may vary and may span a higher range, e.g., up to 10 kHz or higher. The elongated medium 102 may act as a vibro-acoustic filter. Stated otherwise, within some frequency bands, the elongated medium 102 may not influence the vibro-acoustic waves travelling therein (in its structure and / or fluid content). At some specific frequencies or within specific frequency bands, the elongated medium 102 may induce changes to a vibro-acoustic wave travelling therein. The vibro-acoustic wave maypropagate in the elongated medium 102 and may “store” or "carry" structural information associated with the elongated medium 102 that vibrates. The generated input signal 112 may thus act as a carrier of the information to be extracted from the excited elongated medium 102. The generated input signal 112 may thus be referred to as a carrier signal. In order to carry the most efficiently the information, the vibro-acoustic properties and / or dynamic response of the elongated medium 102 may be accounted for in the generation of a suitable vibro-acoustic excitation. In other words, a generated input signal 112 that is adapted to the dynamic response of the elongated medium 102 is therefore contemplated. The dynamic response of the elongated medium 102 may be determined via a modal analysis. The modal analysis may allow to identify (or localize in the frequency domain) the specific frequencies (or eigenfrequencies) and the associated shape of deformation of the elongated medium 102. The modal analysis may be performed via finite elements simulations or experimentally through measurements. The vibro-acoustic excitation may be specifically selected (“tuned” or “built”) to excite the elongated medium 102 by varying the frequency information of the vibro-acoustic excitation, the type of excitation, the duration, etc. The generated vibro-acoustic excitation may be refined iteratively until a desired quality of the signal sensed at the sensing units 200a, b,c is obtained. It will be understood that the term “vibro-acoustic properties” used herein may be representative of the properties of the dynamic response (which may be referred to as “dynamic properties”), and vice-versa.

[0041] The input signal 112 may include one or more sets of tones, i.e., sets of given frequencies, as a way of exciting the elongated medium 102 dynamically. The length of the tones in time is generally longer than the time needed for the tones to propagate through the elongated medium 102. In such case, the entirety of the elongated medium 102 (or inspected section thereof) may be excited by the tones simultaneously. In practice, a plurality of tones of different frequencies may be sequentially provided to the elongated medium 102 to create various types of excitation patterns. By measuring the correlation between the output signals measured by the sensing units 200a, b,c, it is possible to obtain different structural information respective to excitation patterns created by corresponding tones. It will be appreciated that using tones to excite the elongated medium 102 and measuring the output signals at a plurality of locations on the elongated medium 102 is generally suited for characterizing non-linear systems.

[0042] In at least some embodiments, the tones are obtained from a dictionary (also called “library”) comprising a plurality of tones selected to create a variety of excitation patterns in the elongated medium 102. In a case where the elongated medium 102 is characterized iteratively and / or the vibro-acoustic excitation refined iteratively, the first iteration may include exciting the elongated medium 102 with vibro-acoustic waves including the entirety of the dictionary. For the next iterations, tones may be selected in the dictionary to extract specific structural information from the elongated medium 102 obtained in the first iteration without needing to reproduce the entire dictionary. The dictionary may be generic, i.e. , not configured for creating excitation patterns for specific types of elongated media, or specific to the elongated medium 102 subject to the characterization. In the latter case, the dictionary may be created based on analytical and / or experimental modeling of the elongated medium 102.

[0043] In one specific embodiment, the input signal 112 is a pre-defined signal formed of intervals of tones and no signal periods performed sequentially. For instance, the input signal 112 may include a 20 Hz tone played for five seconds, followed by a ten seconds of no signal, followed by a 40 Hz tone played for five seconds, followed by a ten seconds of no signal, followed by a 60 Hz tone played for five seconds, followed by a 80 Hz tone played for five seconds, followed by a ten seconds of no signal followed by a 100 Hz tone played for five seconds, followed by a ten seconds of no signal followed by a 120 Hz tone played for five seconds, followed by a ten seconds of no signal.

[0044] These pre-defined signals may be used for a plurality of elongated media, and thus be considered generic.

[0045] It will be understood that the present disclosure is not limited to tones, as the input signal 112 may include other types of signals. In one embodiment, the input signal 112 includes a broadband signal in which a plurality of tones are convoluted.

[0046] In other embodiments, the input signal 112 includes a sweep signal having a continuous increase in frequencies. The time at each frequency is at least greater than the time required for the input signal 112 to propagate through the elongated medium 102. In a specific embodiment, the input signal 112 may include a sweep signal starting at 5 Hz and ending at 120 Hz with increments steps of 5 Hz and with a residence time of 5 seconds for each frequency. In another specific embodiment, the input signal 112 may include a chirp-type signal having first sweep signal starting at 5 Hz and ending at 10 Hz, a second sweep signal starting at 5 Hz and ending at 15 Hz with an increment step of 5Hz, a third sweep signal starting at 5 Hz and ending at 20 Hz with increment steps of 5 Hz and so on.

[0047] In operation, the sensing units 200a, b,c are distributed along the elongation axis X and are spaced apart by a constant or varying distance. Such distance may be predetermined, or determinable by geolocation. In at least some embodiments, the sensing units 200a, b,c are positioned at the same longitudinal position between adjacent ones of them, but with a different angular position from one another, though they could have a same angular position. In operation, the sensing units 200a, b,c are configured to measure vibro-acoustic waves propagating in the elongated medium 102. It will be appreciated that the number of sensing units 200a, b,c is not limited to the count of three (3) as depicted in Fig. 1, as any number of sensing units that is more than one (1) may apply, in accordance with various embodiments. The sensing units 200a, b,c will be further described hereinafter.

[0048] Each of the sensing units 200a, b,c are communicatively coupled to the computing device 106. The computing device 106 is configured to receive signals indicative of a vibro-acoustic property, or dynamic response, from the sensing units 200a, b,c. Another way of expressing this is that the computing device 106 is configured to receive signals from the sensing units 200a, b,c, from which vibro-acoustic properties of the elongated medium 102 may be derived. Such signals will be referred to herein as output signals that may be used as part of a single input multiple outputs (SIMO) characterization of the elongated medium 102.

[0049] The computing device 106 may be in wired communication with one or more of the sensing units 200a, b,c, or in wireless communication. In some embodiment where the computing device 106 is in communication with a user interface 108, the latter may be, for instance, a mobile device such as a tablet or smart phone, in order to monitor and / or visualize the signals received from the sensing units 200a, b,c. Visualization of the signals may be in the form of one or more graphs, diagrams (e.g., cross-correlation spectrograms), or other visual representation, and / or a visual indicator, such as an icon or other identifier indicative of a presence or absence, and / or acquisitioning quality indicator of one or more of the output signals from the sensing units 200a, b,c. Indication of the quality of a signal may be, e.g., a given value of a signal to noise ratio, the presence of an input signal 112 in the measured signal, a given value of coherence between signals measured at different outputs and the like. If such indications are not obtained by thecomputing device, a prompt may be provided to the user interface 108 indicating that the quality of the signal is not sufficient for representative measurements. In at least some embodiments, the computing device 106 may form part of the user interface 108 (or vice versa) or part of at least one of the sensing units 200a, b,c or the vibration generator 104.

[0050] Referring to Fig. 2, a sensing unit 200, such as the sensing units 200a, b,c described above, includes at least a sensor 202, and a processing unit 204. Optionally, the sensing unit 200 may include a geolocation identifier 206. The sensing unit 200 is configured for acquisitioning a dynamic response of the elongated medium 102 excited by the input signal 112 generated by the vibration generator 104. In at least some embodiments, the sensor 202 is configured to create an impedance matching at a contact point between the sensing unit 200 and the elongated medium 102. In other embodiments, the impedance matching is created between the vibration generator 104 and the elongated medium 102. The sensing unit 200 may have a data storage functionality so as to store at least part of the data associated with the measured dynamic response in the processing unit 204. Such data may be communicated via the output signals from the sensing unit 200. It should be understood that the sensor 202 and the processing unit 204 may be integrated together, i.e., not necessarily distinct components of the sensing unit 200.

[0051] The sensor 202 is configured to detect and measure vibro-acoustic signals. In operation, the sensor 202 is configured for transducing a vibro-acoustic signal propagating at the surface or in the bulk of the elongated medium 102 and measured at an output point, into an electric signal. In at least some embodiments, the sensor 202 includes an accelerometer. The accelerometer may be in the form of a piezoelectric sensor. In other embodiments, the sensor 202 includes a dynamic response sensor such as a displacement sensor, a velocity sensor, a strain gauge and the like. The sensor 202 may be a microelectromechanical system (MEMS), in some cases. In at least some embodiments, the sensor 202 may include an array of transducers. Other sensors 202 suitable to measure vibro-acoustic signals may be implemented in the sensing unit 200.

[0052] The vibro-acoustic signal measured by the sensor 202 is processed into an output signal, which may be stored in the processing unit 204 and / or conveyed to the computing device 106. The output signal is representative of the vibro-acoustic properties of the elongated medium 102 or allows to derive such vibro-acoustic properties via processing. The output signal is retrievable by the computing device 106.

[0053] The geolocation of the sensing unit 200 may be required for obtaining a geographical mapping of the dynamic behavior of the elongated medium 102. As described above, the sensing unit 200 may include a geolocation identifier 206, preferably a global positioning system (GPS) antenna or node for obtaining the geolocation coordinates of the sensing unit 200. The coordinates may allow to measure a distance between respective locations of the sensing units 200. The sensing unit 200 may be configured to convey a geolocation signal indicative of a location of the sensing unit 200 via the geolocation identifier 206, though this is optional. In at least some embodiments, the coordinates are stored in the processing unit 204 or in the computing device 106. In other embodiments, the coordinates are obtained by associating the location of the sensing unit 200 using a map. In other embodiments, the coordinates are relative to the coordinates of other sensing units 200. In some variants, the coordinates may be obtained by measuring a distance from a reference location using, for example, a measuring wheel or a laser distance measurer.

[0054] Figs. 3 and 4 illustrate embodiments of a system 300,400 for characterizing an elongated medium 302,402. The systems 300,400 and elongated medium 302,402 may correspond to the system 100 and elongated medium 102 describe above. It should be understood that the features discussed above with respect to system 100 and elongated medium 102 similarly apply to the systems 300,400 and elongated medium 302,402 and will therefore not be repeated herein for conciseness. In Fig. 3, the system 300 includes a vibration generator 304 connected to an outer surface of the elongated medium 302. In the embodiment shown, the elongated medium 302 is a pipe having pressurized fluid therein. A plurality of sensing units 200, here two, each have a sensor 202 connected thereto. As illustrated, the elongated medium 302 could have a defect 306 and a leak 308, which are represented between the two sensing units 200d,e, along an elongation axis X. In practice, such defect 306 and leak 308 may not be known prior to implementing the characterization of the elongated medium 302. It will be appreciated that, as shown, the vibro-acoustic signal generated by the vibration generator 304 may propagate through the elongated medium 302 and interact with the illustrated defect 306 and the leak 308. Such interaction may alter the properties of the propagating signal, or signal “signature”. The propagated vibro-acoustic signal measured at the sensing units 200 may therefore embed structural information on the elongated medium 302 that includes the alteration caused by the defect 306 and the leak 308. It will be appreciated that various other types of anomalies can be detected using the system 300, such as deformation of the elongated medium 302,mineral buildup inside and / or outside the elongated medium 302, stiffness variation in various portions of the elongated medium 302 and the like.

[0055] As illustrated in Fig. 4, in a data gathering application, the system 400 is adapted for characterizing a pipe network 402, which may be in a particular case a fire hydrant network. The system 400 includes a plurality of sensing units 200f,g,h,i,j, here five though other numbers are possible, each connected along an elongation axis X to the pipe(s) of the pipe network 402, and a vibration generator 404 connected to a hydrant of the pipe network 402. In other embodiments, the vibration generator 404 may be connected to other interfacing components of the hydrant network, for example an intermediary component between the vibration generator 404 and the hydrant, on a pipe segment, a valve or an access chamber in fluid flow communication with the elongated medium 302 or other contact points on components serially connected to the elongated medium 302. The vibration generator 404 could also be connected to a pipe of the pipe network 402 or other interface components as described above. While the system 400 is adapted to be installed on a pipe network 402 such as fire hydrant network, which includes usually a distribution watermain composed of small pipes, the system 400 may be also installed on transmission mains, which are composed of larger pipes. The present technology may thus be implemented in various sorts of pipe network, regardless of the diameter of the pipe.

[0056] The sensing units 200f,g,h,i,j are communicatively coupled to a computing device 406, such as computing device 106 described above, for conveying output signals indicative of measured vibro-acoustic properties of the pipe network 402 (or from which these properties may be derived). A user interface 408 may also be connected to the computing device 406 for monitoring and / or visualizing the output signals received from the sensing units 200f, g,h, I ,j. Visualization of the signals may be in the form of one or more graphs, diagrams, or other visual representation, and / or a visual indicator, such as an icon or other identifier indicative of a presence or absence, and / or an acquisitioning quality indicator of one or more of the output signals from the sensing units 200f,g,h,l,j, for visualizing the output signals or characteristics thereof. The processing of the output signals by the computing device 406 may be part of the system characterization of the pipe network 402. The characterized system may be visualized on the user interface 408. The characterized system may comprise information (e.g., characteristics) on various portions of the pipe network 402, e.g., the flow rate and the pressure in the pipe(s), thepresence of defects, mineral buildups and / or leaks in the pipe network 402 and the like. In one embodiment, the user interface 408 may be a mobile device, such as a tablet or smart phone. Other devices may be contemplated, such as a portable computer or a computer station.

[0057] The output signals received from the sensing units 200 may be computed so as to create, or at least rectify an analytical model of the elongated medium 102 and / or characterize a dynamic response of the elongated medium 102 to one or more input signals 112, as will now be further described. A method for analyzing vibro-acoustic properties of the elongated medium 102 or a pressurized fluid system including such elongated medium 102 will be described.

[0058] An analytical model of the elongated medium 102 or the pressurized fluid system may first be computed. The analytical model (or “digital twin”) of the elongated medium 102 may assist in determining what input signal(s) 112 should be generated to reveal information on the elongated medium 102. The analytical model may also be used to compare measured data or full system characterization as described below, with an expected dynamic behavior from the physics of the dynamic behavior of the elongated medium 102. The analytical model is intended to correspond to a digital twin of the physical elongated medium 102 to be diagnosed / characterized. In order to build the digital twin, information on the pressurized elongated medium 102 may be collected. Based on the collected information on the pressurized elongated medium 102, including mechanical properties of the elongated medium 102, the digital twin may be built. Such a digital twin can be built via software, such as COMSOL®. The digital twin of the elongated medium 102 can be built based on the specification sheet of the buried pipe. While there may be variations between the specification sheets and the properties of the actual elongated medium, e.g., manufacturing variability, the digital twin can provide a sufficiently reliable estimation of the properties of the elongated pipe 102 as a starting point for the methods described herein. The digital twin may be used to simulate the dynamic behavior of the elongated medium 102, by varying one or more parameters of the digital twin and estimate the impact of such parameter(s) on the dynamic behavior of the elongated medium 102. The analytical model may include the computation of various coefficients, and / or mechanical properties of the material of the elongated medium 102, such as the geometry, the tensile stress, the mass, the level of damping, the modulus of elasticity (E) (e.g., Young’s modulus), a level of stiffness, the sound absorption coefficient, the thermalexpansion coefficient, as some examples. In some cases where the elongated medium 102 is a prestressed concrete pipe, tensile stresses induced by steel wire may be taken into account in the analytical model. The analytical model may also include the computation of dimensions and account for the geometry (constant or variable) of the elongated medium 102. In an embodiment, the analytical model may be generated, at least in part, using a finite element analysis (FEA) method and / or a boundary element analysis (BEA). In one embodiment, the model is generated using a Monte Carlo method. In at least some embodiments, the model is generated using artificial intelligence (Al) such as machine learning and / or deep learning techniques. Based on the analytical model, an estimated dynamic behavior of the pressurized elongated medium 102 or the pressurized fluid system may be characterized. Absent measurements on the elongated medium 102 physically, a digital twin of the elongated medium 102 can therefore be used as a reference base to identify or at least estimate structural modes of the elongated medium 102. Refinement of the digital twin of the elongated medium 102 can be achieved by validating the model through physical measurements on the elongated medium 102.

[0059] In at least some embodiments, the analytical model includes the computation of coefficients of fluids propagating inside and / or outside the elongated medium 102, e.g. density (p), specific heat, viscosity, modulus of compressibility (K), etc. A recognized mathematical model in the field of vi bro-acoustics has been established by J. M. Muggleton, M. J. Brennan and R. J. Pinnington in the scientific publication entitled “Wavenumber Prediction of Waves in Buried Pipes for Water Leak Detection,” published in the Journal of Sound and vibration (2002) 249(5), pages 939-954, the content of which is incorporated herein for reference. This publication present the following equation derived from the equilibrium of forces relationship, which can be used to model the dynamic behavior of a cylindrical elongated medium:

[0060] where kL, ks, kf, ks, kdkds, krand ksare the compressional, shear, fluid, internal radial, external longitudinal, internal longitudinal, external shearand internal shear wavenumbers, respectively, v is the Poisson ratio, a is the radius, Bfand Bmare the bulk moduli of the internal and external media, respectively, Gmis the shear modulus of theexternal medium, E is the Young’s modulus, h is the thickness of the wall and J0,JQ' and H0, HQ are the Bessel functions and Hankel functions of order zero, respectively. Using eq. (1) it is possible to solve the mathematical model for at least two types of waves, namely s=1 and s= 2, which correspond to a fluid dominated wave and an axial shell dominated wave, respectively.

[0061] For s=1 (equation (2)) and s=2 (equation (3)), the general equation (1) of the dynamic behavior of a cylindrical elongated medium becomes, respectively:

[0062] Where k is the fluid dominated wave wavenumber, k2is the axial shell dominated wave wavenumber, p is the density of the shell material and t is the angular frequency. In at least some embodiments, the compressional wavenumber kLmay be represented by the following equation:

[0063] The fluid dominated wave (s=1) may generally propagate along a longitudinal axis of the elongated medium 102 and oscillates orthogonally to the longitudinal axis, and is thus sensitive to and highly dependent of the modulus of elasticity and Bulk modulus of the material it traverses, e.g., the fluid, the wall of the elongated medium 102 and the soil surrounding the elongated medium 102 when underground. The axial shell dominated wave (s=2) is usually confined within the wall of the elongated medium 102, and its propagation is typically less affected by or dependent on the modulus of elasticity and Bulk modulus of the fluid and the soil surrounding the elongated medium 102 when underground. As such, in at least some embodiments, the sensing unit 200 may measure at least one of the fluid dominated wave and the axial shell dominated wave, preferably both. It will be appreciated that both waves may coexist at the same time and have different speeds of propagation in the elongated medium 102. In such case, frequential separation may occur (e.g., through data processing, filters). In some cases, the separation between the frequency ranges may not be total, as overlaps can exist betweenthe frequency ranges. Deconvolution algorithms can be used to separate the two waves from the measured signal if an overlap occurs. In other cases, the frequency ranges may not overlap, and the two waves can be extracted from the measured signal by either separating the signal in timeframes or filtering the signal in frequency.

[0064] The dynamic behavior of the elongated medium 102 may thereafter be modelled using properties inferred from the measured waves at input(s) and output(s) locations along the elongated medium 102. The modulus of elasticity, the Poisson ratio and / or the density of the wall of the elongated medium 102 may be entered into the model to simulate the dynamic behavior of the elongated medium 102.

[0065] In some cases where the elongated medium 102 is a metallic pipe, in which case the modulus of elasticity of the pipe is substantially larger than the modulus of elasticity of the surrounding soil and of the fluid, the fluid dominated wave is generally predominant in the measured output signals. In such cases with metallic pipes, the fluid dominated wave can be measured in frequency bands ranging from 0 Hz to 3,000 Hz. Measurements of the fluid dominated wave in such situation can be made over large distances along the elongated medium 102 since the fluid dominated wave tends to attenuate less rapidly because of the high stiffness of such pipes. On the other hand, for metallic pipes, the axial shell dominated wave is rapidly attenuated by the pipe over a relatively short distance, and the presence of the axial shell dominated wave in the measured signal may thus be less or not visible at the signal output locations along the elongated medium 102, unless signal output locations are very close from each others, such as a few meters away from each other (e.g., less than 10 meters). As such, the use of a fluid dominated wave for characterizing a metallic pipe may be preferable, according to the configuration of the pipe.

[0066] In other cases, the elongated medium 102 may be a plastic or polymer pipe, a plastic pipe network, or polymer pipe network which is generally less stiff than metal. As such, the fluid dominated wave, when propagating in plastic or polymer pipes, is more attenuated or “absorbed” by the pressurized fluid system compared to cases where the elongated medium is a metallic pipe. In addition, because of the dynamic properties of plastic or polymer pipes, including its lower modulus of elasticity and flexural modulus, the fluid dominated wave may be measurable on lower and narrower frequency bands, e.g., between 0 Hz and 200 Hz. The modulus of elasticity of the pipe may be similar to the modulus of elasticity of the soil. On the other hand, when propagating in plastic or polymerpipes, the axial shell dominated wave is able to propagate with less losses than the cases where the elongated medium 102 is a metallic pipe, because the dynamic properties of the wall of the plastic or polymer pipes cause less absorption (attenuation) of the axial shell dominated wave in such medium. As such, for plastic or polymer pipes, measuring axial shell dominated wave in the output signals can be achieved in relatively low frequency bands, e.g. between 200 Hz and 2,000 Hz compared to axial shell dominated wave in metallic pipes which would be seen at more than 3000 Hz. To summarize, depending on the nature of the elongated medium 102, the output signal may comprise different types of waves on a given set of frequency bands.

[0067] Yet, in other cases, where the elongated medium 102 is a prestressed concrete pressure pipe (PCCP) having a steel core cylinder with concrete layers inside and outside, the fluid dominated wave may reveal the overall pipe hoop stiffness of the layered pipe design, while the axial shell dominated wave may reveal structural information on the integrity of the steel core cylinder.

[0068] In at least some embodiments, the parameters required for modelling the dynamic behavior of the elongated medium 102 are the modulus of elasticity, the density, the Poisson ratio, the wall thickness and the diameter thereof. As such, when the output signal comprises information related to the fluid dominated wave and the axial shell dominated wave, it is possible to generate an experimental model using a mathematical model including equations (2) and (3). Due to the physical nature of those waves, assumptions must be made in order to reduce the number of parameters to remain with a single unknown parameter. Generally, by assuming a theoretical value on the modulus of elasticity in the equation of the fluid dominated wave, and a theoretical value of the thickness of the pipe in the axial shell dominated wave, it is possible to simulate the dynamic behavior of the pipe and derive a stiffness profile of the pipe, using each equation independently. Stated otherwise, it may be possible to obtain the dynamic properties of the elongated medium 102 using only one of equations (2) and (3), using assumptions. Since assumptions are made on the properties of the wall of the elongated medium 102 instead of measurement of these characteristics, using only one of equations (2) and (3) may be limiting in terms of analytical accuracy. Indeed, both the fluid and the mechanical properties of the elongated medium may play a role in how the waves propagate. The coupled wave equation of motion governs the propagation of acoustic waves through a material medium that interacts with the structure of the elongated medium, such as aviscoelastic pipe containing fluid. By combining both equations (2) and (3) in a linear or non-linear system, it is possible to get rid of those assumptions and thereby obtain a dynamic behavior of the pipe that is not or quasi not based on theoretical values. The combined fluid-structure interaction (elongated medium and fluid therein) involves solving the wave equation for both the elongated medium and the fluid. In such case, the eigenfrequencies can be obtained via experimental modal analysis or numerical modelling. As mentioned above, the proposed method requires a suited elongated medium 102, such as a plastic or polymer pipe, or metallic pipes with a smaller distance between the signal input location and signal output locations (or between adjacent signal output locations) in order to be able to adequately measure both fluid dominated and axial shell dominated waves. As such, the positioning of the sensors may be selected as a function of the mechanical properties of the elongated medium 102, such as its stiffness, or its sizes / dimensions.

[0069] In an embodiment, exciting the plastic or polymer pipe and sensing axial shell dominated wave and fluid dominated wave in the plastic or polymer pipe, and then solving the mathematical model based on equation (2) and equation (3) above may provide information on the stiffness and thickness of the pipe along its length that would otherwise not be possible to obtain by relying only on the fluid dominated wave and related signal data. It was found that for plastic or polymer pipes, since the axial shell dominated wave is within a lower frequency range than for metallic pipes, exciting the elongated medium 102 to induce resonance in such lower frequency range may produce sufficiently reliable data to characterize dynamically with sufficient precision hundreds of meters of plastic or polymer pipe based on a single input and multiple output characterization as described above.

[0070] In practice, an input signal 112 may be injected in the elongated medium 102 and vi bro-acoustic resonance may be induced in response to the latter. This resonance may include harmonic vibrations that span in wide ranges of frequency bands and generate various types of waves. The resonance may, in at least some embodiments, generate fluid dominated waves and the axial shell dominated waves. In other words, the amplification by vibro-acoustic resonance of various harmonics of the elongated medium 102 may generate various types of waves in the elongated medium 102, including fluid dominated waves and the axial shell dominated wave. The signal measured by the sensors generally may comprise the input signal 112 and the generated resonance.Measuring both waves induced by the resonance or other types of induced vibrations in the elongated medium 102 may provide distinct sets of data which may be processed to obtain the characteristics of the fluid and the characteristics of the wall of the elongated medium 102. The sets of data may be combined (prior to or after they are processed). As part of the characterizing method, when generating the experimental model, the respective measured output signals may be normalized with the input signal in order to remove the input signal from the experimental model.

[0071] Inducing more resonance, thus causing more signal amplification, by injecting an input signal 112 tuned based on the dynamic properties of the elongated medium may allow to extract more reliable information on the elongated medium 102. While a preferred excitation is one that may create vibro-acoustic resonance in the elongated medium 102 by targeting the structural natural frequencies of the elongated medium 102 for obtaining the dynamic response thereof, it will be appreciated that other types of excitations, such as excitation of modes of vibration not targeted towards the structural natural frequencies of the elongated medium 102, may be contemplated. It will be appreciated that the modes of vibration (structural modes) may vary, and be stationary or propagating, longitudinal and / or transverse and include fundamental modes and / or higher harmonics. In at least some embodiments, a single mode of vibration may be excited in the elongated medium 102, though more than one mode could also be. A method to excite an elongated medium, such as a pipeline, on a per mode of vibration basis will be described herein.

[0072] At least one or a plurality of vibration generators 104 coupled with the elongated medium 102 may be used to generate a vibro-acoustic signal. The vibro-acoustic signal may be selected to excite the elongated medium 102 at least in an axial shell dominated wave frequency range. Such range can be known by analytical modelling (digital twinning) and / or theoretical properties of the elongated medium 102, for example. In the plastic or polymer pipe(s) application, a vibro-acoustic signal may be generated, with such vibro-acoustic signal being configured to induce resonance in the elongated medium 102 that will include the fluid dominated wave and the axial shell dominated wave. The first vibro-acoustic signal along with the induced resonance may be sensed by the sensing units 200 along the elongated medium 102 at the input location (if a sensing unit 200 is present at the input location) and respective output locations away from the input location along the elongated medium 102. The acquired signal data may be stored in the sensing units 200 and / or computing device 106. By processing of such acquired signaldata, the mathematical model defined by equation (2) and (3) described above may be solved. An experimental model of the elongated medium may be generated based on the solved mathematical model. Such experimental model may represent or be used to represent the dynamic behavior of the elongated medium 102. Such method for characterizing dynamically the elongated medium 102 may be repeated iteratively to compare the generated experimental models and verify their correlation. The correlation between successively generated experimental models may be used as a quality indicator of the input, output and experimental model obtained. In at least some embodiments, the vibro-acoustic signal generated by the vibration generator(s) 104 may be subtracted (e.g., by normalization, deconvolution) from the signal sensed by the sensing units 200. In such case, the signal measured by the sensing units 200 may be representative of the response of the elongated medium 102 rather than to the excitation signal injected in the elongated medium 102.

[0073] Once an experimental model has been generated as described above, it is possible to generate one or more additional experimental model by selecting a second input signal that is based on the quality indicator of the first experimental model, which can be established, e.g., by the signal to noise ratio of the measurements over the frequency bands (i.e., the elongated medium 102 is excited in vibration, and the signal propagates), or correlation, as mentioned, or based on information derived from the dynamic behavior computed from the first pass or series of experimental models, e.g., frequency, discrete frequencies, or frequency range with the highest signal amplitude from a modal analysis on the experimental model. For example, a low signal-to-noise (SNR) ratio with a first input signal may indicate that the first input signal did not provide an optimal vibratory response and / or sufficient signal propagation. In such cases, a second input signal could be used, for example at an additional access point along the elongated medium 102 if the access point at which the first input signal was injected would not allow a good contact between the vibration generator 104 and the elongated medium 102. As another example, a second input signal could be used with an increase energy (or amplitude) to maximize the response and ensure a good SNR, and / or by adjusting the frequency content to maximize the bandwidth between the input signal and the measured response.

[0074] As such, another vibro-acoustic signal different from that generated in the first pass or first series of experimental model generation may be generated via the vibrationgenerator(s) 104 at the input location (same input location as the first vibro-acoustic signal) to induce resonance in the elongated medium 102. For example, such other vibro-acoustic signal may be selected to target resonance corresponding at least to the frequencies or frequency range of the fluid dominated wave signal and / or the axial shell dominated wave signal. The vibration generator(s) 104 may then generate such other vibro-acoustic signal. The measurements of the signals made at the input location and at output locations along the elongated medium 102 may be processed to further generate an additional iteration of experimental model. Once such additional iteration of experimental model has been generated, it is possible to compare the experimental models derived from some or all of the vibro-acoustic signals generated and measured iteratively as mentioned above. This step can be used to further refine new input signals to be generated in the elongated medium 102, or as a validation method to confirm the adequacy of the digital twin and / or experimental model built, for example.

[0075] As part of the dynamic characterization method described herein above, the experimental model(s) may be plotted as a stiffness profile, which can include a normalization of the stiffness profile based on a nominal stiffness of the elongated medium 102, in some instances. Such nominal stiffness may be based on an analytical model. The plot can also include a visualization mean to identify a stiffness differential between the nominal stiffness and the stiffness profile.

[0076] A full system characterization may be performed in terms of transmissibility from one output point to another (i.e. , location of the sensing units or extraction point of the measured vibro-acoustic signals), cross-correlations (or any other comparison-type of processing) between output signals, cross-correlations (or any other comparison-type of processing) between an input signal and the respective output signals, transfer functions between the input signal and the respective output signals, or a combination thereof. In at least some embodiments, dynamic time warping, root-mean-square error, instantaneous phase synchrony, cross-spectral density, coherence and / or autocorrelation algorithms are performed to characterize the model. The full characterization may provide measured vibro-acoustic properties of the pressurized fluid system, such as through processing or post-processing. Once a full characterization of the pressurized fluid system is computed, the expected dynamic behavior from the analytical model (digital twin) may be compared with the measured vibro-acoustic properties.

[0077] Now referring to Figs. 5A-5C, there are shown cross-section illustrations of elongated media 500, 520, 540, which represent a metallic pipe 500, a plastic pipe 520 and a PCCP 540, respectively. The metallic pipe 500, as shown in Fig. 5A, is a conduit that generally has, in practice, a degradation that is due to corrosion of the wall 502 overtime. The plastic pipe 520, as shown in Fig. 5B, has generally, in practice, a degradation due to a change of ductility of the material and deformation of the cylinder pipe, also known as ‘ovality’ or ‘out-of-roundness’. This may translate into brittleness of the pipe, cracking or perforation of its wall 522, or fatigue thereof. A PCCP 540, as shown in Fig. 5C, is a complex structure that has several subcomponents, such as, but not limited to, an inner concrete layer 542, a metallic layer 544, an outer concrete layer 546, a wiring layer 548 and a mortar layer 550. Each layer 542, 544, 546, 548, 550 may have its own type of degradation or degradation behavior. The elongated media 500, 520, 540 shown in Figs. 5A-5C are exemplary only and provided only for context.

[0078] A mode of vibration of the elongated medium 500, 520, 540, can be affected by a degradation of the elongated medium 500, 520, 540. Since a degradation of the elongated medium may change the structural integrity or properties of the elongated medium, such a degradation can have a direct impact on one or more modes of vibration of the elongated medium 500, 520, 540. By targeting a mode of vibration of the elongated media 500, 520, 540, and tracking its variation in frequency, it is thus possible to evaluate a level of degradation (or reinforcement) of its structure. The tracking can be made by computation of information / data derived from the processing of the dynamic response. For example, a delta between frequency values can provide information on the extent of deviation (shift) , and such delta may correlate with the level of degradation of the structure. The tracking may also involve a visualization of the frequency value delta on a graph or other visual representation. The deviation can be revealed by visual analysis of the data or computation of data, among other possibilities. As the expected resonant frequency for a targeted mode of vibration for a non-degraded elongated medium may provide information on the wall thickness of such elongated medium, through physics, an estimated wall thickness of the elongated medium in its actual state may be derived from the resonant frequency obtained from measurements on the elongated medium. As an example, a degradation or failure of a metallic pipe 500 that may typically be seen is a reduction of wall thickness, often due to corrosion. A frequency lower than expected for the targeted mode of vibration of the metallic pipe 500 can be indicative of a reduced thickness of the wall. Similarly, a frequency higher than expected for the mode of vibrationof the metallic pipe 500 can be indicative of a reparation or a reinforcement of the wall. For a homogeneous material such as a metallic pipe, when the pipe is degraded (loss of wall thickness), all the vibration modes associated with the circumferential deformation of the pipe will decrease in frequency. By targeting, individually, modes of vibration associated with the circumferential deformation of the pipe, and tracking their respective variation in frequency, a presence of a deviation for all such modes can be an indicator of presence of a degradation (reduction in wall thickness): all modes associated with the circumferential deformation of the pipe may have shifted and decreased in frequency (deviation in frequency). Using the deviation of multiple modes in a same direction in frequency, where such modes can be associated with a same deformation of the elongated medium (e.g., circumferential deformation), can provide a validation mechanism to ensure that a deviation in frequency of a mode of vibration can actually be relied upon to associate with it the presence of a degradation. Identification of the modes associated with a same deformation of the elongated medium can be obtained by modal analysis (e.g., modal analysis from the digital twin of the elongated medium). Similarly, a deviation in the frequency for a mode of vibration of a plastic pipe 520 may also correspond to a change in the condition of the plastic pipe 520. A degradation or failure of a plastic pipe that may typically be seen is a crack and / or loss of stiffness / ductility due to fatigue. A decrease or increase in frequency from a nominal / expected frequency for a given structure can thus provide information on its structural condition.

[0079] In the case of the PCCP 540 (or other complex pipe assembly), one mode of vibration may also decrease in frequency or increase in frequency as a result of a given defect. In addition, ccircumferential deformation of the PCCP will exist, but the modes of vibration associated with it may not be associated with a single sub-component of the PCCP. For example, modes causing the circumferential deformation of the pipe may be modes due to the coupling between subcomponents, or between the fluid inside the pipe and a subcomponent, etc. As such, tracking the deviation of all modes of vibration on a non-targeted manner may not provide information on the structural condition of a subcomponent itself only. Since each subcomponent of the PCCP 540 may have their own modes of vibration, selecting a specific mode of vibration that can be associated with one of the subcomponents and tracking the deviation of the frequency of that mode of vibration can provide information on the structural condition of that subcomponent. By exciting more than one mode at a time (or a plurality of modes in a non targeted manner), drawing inference from a deviation or grouped deviation of the modes could yielderroneous conclusions on the structural condition of the pipe, since some modes could increase in frequency whereas others could decrease in frequency based on a given defect, i.e., the direction of the change may not be the same for all modes. Stated otherwise, one mode may decrease in frequency or increase in frequency based on a given defect. Therefore, on a per mode basis, the deviation (or “shift”) in frequency can be associated with defects. However, since one mode could increase in frequency while another decrease in frequency, the ‘direction’ of change may not be the same for all modes. In this scenario, considering all the modes at once might not provide reliable information about the condition of the structure of a complex, non-homogeneous pipe assembly.

[0080] Here are other reasons why selecting a specific mode of vibration to be excited may provide more reliable information on the condition of the elongated medium. The modes of vibration may also be influenced by a fluid flowing in the elongated medium. The dynamic coupling between the wall of the pipe and the fluid may induce modes of vibration in the response signal. Specifically exciting the coupled mode between water and pipe to assess the condition of the pipe assumes homogeneous characteristics of the water for the assessment to be accurate. This assumption may not be true for the sewer system when the water is not homogeneous. In some cases, for example, the water may not be clean and large particles can be present in the water flowing into the elongated medium (e.g., sewers). Therefore, targeting modes specific to the pipe itself would yield a more accurate assessment of the condition of the pipe. As another example, other components coupled to the elongated medium, such as sensors, valves and the like can also induce modes of vibration in the response signal. As such, exciting several modes of vibration in a non-targeted manner would generate a dynamic response that can be affected by the presence of the various components instead of providing reliable information on the condition of the elongated medium itself, or a subcomponent thereof (e.g., PCCP).

[0081] Based on theory, it is understood that the dynamic behavior of the whole complex structure can be formed of the dynamic behavior of each subcomponent. If we extract a mode on the assembly, we can associate such mode of vibration to a subcomponent or a coupling between subcomponents. In at least some applications, the whole complex pipe assembly (e.g., PCCP) can be characterized, for example experimentally, or by finite element analysis. A model may be generated by dynamically characterizing one specific layer, e.g., the metallic layer 544, and dynamically characterizing the combined metalliclayer 544 and concrete layer(s) 542, 546, on the assumption that these material can be considered homogenenous. This could allow to determine the modes of vibration intrinsic to the metallic layer, and the modes of vibration from the coupled metallic / concrete layer. Based on a model defined by a metallic layer and a concrete layer, we may obtain a sufficiently reliable model of what would be a pipe without wiring layer 548. By subtracting the dynamic behavior of the metallic layer and the dynamic behavior of the coupled metallic / concrete layer(s) from the dynamic model of the whole complex pipe assembly, the dynamic behavior associated with the wiring layer 548 may be found, or at least estimated. Obtaining / estimating such dynamic behavior of the wiring layer 548 may then allow to identify / estimate the modes of vibration that are associated with it. The PCCP 540 may then be excited by a vibro-acoustic signal suited for exciting one of the modes of vibration of the wiring layer 548 (or a plurality of modes of vibration thereof) in order to obtain information on the condition of that layer 548.

[0082] It is possible to compare, in the frequency domain, modes of vibration obtained from signal processing with the theoretical or analytical modes obtained from a digital twin, as mentioned herein above. Such model could be a theorical, analytical and / or finite element model of the elongated medium, for example. The modes obtained from the signal processing may then be associated with the modes of vibration identified / estimated from the digital twin. A deviation in frequency between the modes obtained from the signal processing and the modes of vibration identified / estimated from the digital twin and excited in the elongated medium can then be tracked (e.g., identify a delta in the respective resonant frequencies for respective modes of vibration of interest). From such deviation, a change in the structural condition of the elongated medium or subcomponent thereof can be inferred.

[0083] In some applications, a deviation of the frequency may also be tracked over time, for example at different point in time (e.g., monthly, yearly), using the same vibro-acoustic signal to excite the mode of vibration of interest. A progressive degradation of the subcomponent could be detected if the magnitude of the deviation changes over time for that targeted mode(s) of vibration.

[0084] Without relying on a model (e.g., finite element analysis model) to identify / estimate the modes of vibration of interest, e.g., the modes that are associated with a specific subcomponent of the PCCP, an experimental model could be generated by data processing. In such case, as a first step, it would be desirable to excite all modesof vibration of the elongated medium (all modes that are feasibly excitable using the system 100, 300, 400) to have a picture of the dynamic behavior of the elongated medium as a whole. By doing so, peaks of resonance may be identified and associated with respective modes of vibration of the elongated medium and / or resonant frequencies of such modes. Then, by analyzing each mode one after the other, once analyzed, it may be possible to identify the modes of vibration that provide similar information on specific defects or deterioration mechanisms but with a greater resolution. It may be required to process the signal using suited algorithms, e.g., deconvolution algorithms, peak finding algorithms, empirical modal decomposition algorithms, band-pass analysis algorithms, and modal analysis in order to identify the modes of vibration that provide relatively the same information with a different resolution. The ‘information’ that is being referred to here can be the mode of deformation (or “mode shape”) of a subcomponent of interest. If, modes of vibration identified are associated with the same mode of deformation of the specific subcomponent of interest, they can be considered as providing the same information but with a different resolution. Once the modes of vibration providing relatively the same information are identified, they can be regrouped. For each regrouping, one may associate a different mechanism of failure of one or more subcomponents of the elongated medium.

[0085] Computing the dynamic response of an elongated medium, such as a pipe, by considering all the modes (vibration and acoustic modes) at once might yield inaccurate or erroneous results, especially on non-homogeneous material pipes or complex assembly pipelines, as mentioned above. One advantage of the excitation on a per mode of vibration basis method is that it can enable the diagnostic of the elongated medium on a single mode of vibration basis. Targeting a resonance mode of the pipe, i.e., an intrinsic characteristic of the pipe, may allow a dynamic response analysis that is focused on an individual dynamic behavior of the pipe (or specific subcomponent thereof) rather than the dynamic response of the whole complex assembly pipelines, which may include valves, joints, and other components, as discussed above, that may have an influence on the structural dynamics locally, and thus affect the accuracy at which properties or the structural condition of interest of the elongated medium can be derived from the processed data.

[0086] As opposed to tracking a variation in the frequency domain of the entire dynamic response over the length of elongated medium (which contains multiple vibrationand acoustic resonance modes), a given specific structural mode of vibration can be tracked in frequency and such variation may be associated with a direct information about the presence of anomalies on the elongated medium and the structural contribution / impact of such anomalies with a resolution dependent on the tracked mode of vibration. In the cases where multiple modes of vibration of the complex assembly pipelines, or subcomponents of such assembly can be excited, an approach of exciting modes one at a time in increasing order of frequency may increase the resolution and therefore improve the precision in identifying the locations of such anomalies. To illustrate this, let’s assume a mode varying between 150 Hz and 200 Hz along a length of an exemplary pipe because of a variation in a metallic wall thickness. The associated resolution obtained from measurements on the exemplary pipe would be proportional to the wavelength for which the formula in the case of a propagating wave is A = c / f where A is the wavelength, c is the speed of sound of the carrier wave and f the frequency of the modes of vibration. As can be seen from this formula, the higher the frequency, the shorter the wavelength and therefore the better the resolution and capability to precisely / accurately locate anomalies. If a higher order mode or harmonic mode is identified for this exemplary pipe, for example varying between 300 and 400 Hz, then the associated resolution at this mode would be twice better than the dynamic response at the previously used mode varying between 150 and 200 Hz. As such, the anomalies on this length of exemplary pipe would be more precisely located using the mode of vibration varying between 300 and 400 Hz. Similarly, if higher order modes can be identified, measured and used in processing, the resolution, precision and accuracy would be better and proportional with the increase in frequency for these modes.

[0087] When multiple modes of vibration are excited, the dominant ones are generally the ones at the lowest frequencies. Combined with wave propagation theory, the lower the frequency, the longer the wavelength, and therefore the lower the resolution. Selecting one mode of vibration at a time to be excited may allow to characterize the elongated medium based on a given resolution, for a given shape of deformation (as modes of vibration contain three pieces of information: frequency, shape / deformation and damping).

[0088] A method to excite an elongated medium, such as a pipe, on a per structural resonance mode basis will now be described. Such method may allow to track the variation in frequency of a specific structural resonance mode without the influence of the complete dynamic response of the elongated medium, i.e., without generating a responsefrom the other structural resonance modes of the elongated medium. This effect can be obtained by building an input signal having a frequency or frequency range matching the targeted mode.

[0089] A given mode of vibration, such as one of a targeted natural frequency or a higher harmonic thereof, may have been selected for its ability to get the desired resolution of the pipeline, or because it allows to relate to a specific sub-component of a complexassembly pipeline such as PCCPs (Pre-stressed Concrete Cylinder Pipes). Since the resolution is proportional to the wavelength for a given pipe, as mentioned above, using higher frequency modes (also known as higher order modes) would lead to shorter wavelengths and therefore better resolution. The selection of the given mode of vibration may be performed from an analytical (digital twin) and / or experimental model. Modes of vibration of sub-components from an assembly can be targeted to characterize a specific sub-component, and therefore diagnose the structural condition of the complex assembly by characterizing the integrity of each of its sub-components individually.

[0090] In order to determine the optimal excitation frequency required to excite a selected mode of vibration, a first excitation of the elongated medium can be made using the techniques described herein (e.g., sets of predefined tones, broadband signal in which a plurality of tones are convoluted, sweep signal having a continuous increase in frequencies, etc.). In some examples, the first excitation signal can be generated from a library of signals, including, but not limited to, a sweep signal with a frequency swipe having a range of frequencies between 0 Hz and 3,000 Hz, for example, to excite a large band of frequencies to start the iterative process of excitation of the elongated medium. A frequency swipe may allow to excite at one point in time one or more natural frequencies of the elongated medium, such that a first estimation of the natural frequencies of the elongated medium can be performed.

[0091] Such a first excitation of the elongated medium can provide output signals. The output signals and the excitation signal, through processing, can then be used to develop the dynamic response of the elongated medium, and, by modal analysis, identify / estimate the eigenfrequencies of the elongated medium. The identification / estimation of the eigenfrequencies may allow to determine an excitation frequency or frequency band for a second pass of excitation of the elongated medium to further acquire output signals along the elongated medium at the output locations, from the excitation of the elongated medium.

[0092] This may ultimately allow to refine the excitation signal that is injected in the dynamic system (elongated medium) to ensure that an optimized excitation signal is used to extract data with respect to the mode of vibration associated with the excitation frequency. The variation of this mode of vibration and / or its associated resonant frequency along the length of the elongated medium can then be tracked (“viewed” or “detected”), as explained above, with more accuracy.

[0093] In some embodiments, a first excitation signal for targeting a selected mode of vibration can be generated based on analytics, e.g., with modal analysis and finite element analysis, by taking theoretical properties of the elongated medium to compute a theoretical dynamic response of the elongated medium containing fluid and extract from said theoretical dynamic response the theoretical natural frequencies (or eigenfrequencies) and mode shapes of the coupled elongated medium and fluid (i.e., the fluid-structure system). A theoretical resonance mode can then be associated to each theoretical natural frequency, thereby forming a starting point of an iterative process of excitation of the fluidstructure system. For example, based on a determination of the theoretical dynamic response of the fluid-structure system, theoretical natural frequencies (theoretical eigenfrequencies) and mode shapes can be identified. The first excitation signal may then be tailored to excite the elongated medium 102 in a frequency range that overlaps and / or include the theoretical resonant frequency of the selected mode of vibration. As mentioned herein, the digital twin of the elongated medium 102 may be used to simulate the dynamic behavior of the elongated medium 102, by varying one or more parameters of the digital twin and estimate the impact of such parameter(s) on the dynamic behavior of the elongated medium 102. In an embodiment, the frequency band width is selected by varying a wall thickness / stiffness of the digital twin to estimate one or more vibration modes and resonant frequencies for a digital twin having such wall thickness / stiffness. For example, calculation of the resonant frequency of a mode of vibration can be performed based on the digital twin for a wall thickness / stiffness of a non-degraded wall down to a wall thickness / stiffness corresponding to a degraded wall (e.g., 10%, 20%, 30%, 40%, 50% wall degradation, or any degradation level in between or beyond). In order to excite only one mode of vibration (and / or a single fundamental mode of vibration and its harmonics) of the elongated medium 102, without the benefit of knowing in advance the actual degradation of the elongated medium, the frequency band width of the excitation signal may be selected to cover a range of resonant frequencies of a single mode of vibration, without overlapping with the resonant frequency of another mode of vibration,corresponding to a range of resonant frequencies calculated from the digital twin’s degraded wall thicknesses / stiffnesses. In some embodiments, the frequency band of the first excitation signal may span over 100 Hz (± 5 Hz). The frequency band could be wider in other embodiments, for example spanning over 200 Hz, 300 Hz, 400Hz, as some possibilities.

[0094] The narrower the frequency band is, the more energy per excitation frequency can be injected in the elongated medium upon exciting the elongated medium via the vibration generator, for a predetermined energy of excitation. Stated otherwise, for a fixed energy of excitation injected in the elongated medium via the vibration generator, an excitation signal having a narrower frequency band will have more energy per frequency than an excitation signal having a wider frequency band. Having a narrower band may also allow a more focused excitation that may less excite other modes that are not to be targeted.

[0095] The first excitation signal tailored as described above (based on information derived from the digital twin, or as described before) can thus be used to excite the elongated medium, via a vibration generator as described herein. The sensing unit may then transduce an output signal at a location along the elongated medium different than the input location of the excitation by the vibration generator. With the transduced output signal(s) at each output signal location and the first excitation signal, a first empirical dynamic response of a segment of the elongated medium between the location of the excitation and one, or more, of the output signal locations can be computed.

[0096] From the first empirical dynamic response, a first set of empirical natural frequencies of the elongated medium can be determined, e.g., by modal analysis. In some cases, from the first set of empirical natural frequencies, a second excitation signal can be built, with such second excitation signal having a frequency band overlapping with and / or including only one empirical natural frequency of the first set of empirical natural frequencies, thereby targeting a single mode of vibration of the fluid-structure system. The band width of the second excitation signal may be adjusted compared to the first excitation signal, e.g., narrower, more selective as to the excitation frequency(ies), etc., to limit mode excitation overlaps. In some cases, for example where the first empirical dynamic response is obtained from a first excitation signal that is tailored based on information derived from the digital twin, the first empirical dynamic response may provide suitable information to be used as part of the processing / post-processing for evaluating thestructural condition of the elongated medium 102.

[0097] Selecting an excitation signal having a narrower frequency band that includes a single empirical natural frequency of the first set of empirical natural frequencies associated with a single mode of vibration may also provide more precision on the determination of the actual natural frequency of the elongated medium, since more energy is canalized for exciting that actual natural frequency. For example, in some embodiments, the range of frequencies of the excitation signal may be reduced to bands surrounding / containing one of the eigenfrequencies, with a bandwidth no larger than 100 Hz, in some cases, between 20 Hz and 80 Hz.

[0098] From the excitation of the elongated medium using the second excitation signal and the output signal at the one or more locations along the elongated medium that have been transduced, a second empirical dynamic response can be computed. Such second empirical dynamic response could also be used as part of the processing / post-processing for evaluating the structural condition of the elongated medium 102.

[0099] Such iterative process can be repeated to generate a third excitation signal, a fourth excitation signal, a fifth excitation signal, and so on. In practice, only a limited number of modes may be excited (e.g., due to capacity and limitations of the vibration generator 104, the quality of the contact between the vibration generator 104 and the elongated medium 102, the characteristics of the elongated medium 102). Because the number of modes that may be excited in a practical scenario may not be known in advance, such an iterative approach may be needed to obtain the information of interest about the dynamics of the elongated medium 102, and refine the excitation signal to ensure that the elongated medium 102 is adequately excited for the purpose of a dynamic response analysis. Once the variation of the empirical natural frequency and peaks of the empirical dynamic response tends to stop varying or substantially not vary (e.g., vary less than a specific frequency range associated with no change in pipe condition from modal analysis) between some of the latest empirical dynamic responses computed, a final (or sufficiently optimized) excitation signal can be determined. The final excitation signal could correspond to the latest excitation signal used to excite and compute the latest empirical dynamic response. The final excitation signal can then be used in one or more subsequent excitation cycle(s) of the elongated medium to acquire a plurality of sets of output signals at each output signal locations for correlation purposes, for example to validate that the signal response obtained is accurate enough to draw reliable information thereof. Todetermine if enough iterations have been done, the quality of the measurements in capturing the modal vibration can then be assessed with similar criteria as described herein above (i.e. quality indicators). A deviation of the frequency of the targeted mode(s) of vibration of the elongated medium, by comparative modal analysis, between the digital twin and the response obtained from data processing and / or comparative modal analysis of the response computed from output signals at different output locations, can then be tracked. From this information, a structural condition (e.g., thickness / stiffness profile) of the elongated medium or subcomponent thereof can be derived, as described above.

[0100] While exciting a given mode of vibration would characterize the elongated medium at a given frequency, and therefore at the associated resolution corresponding to this frequency (as mentioned above), the use of harmonics of such mode of vibration could improve the resolution of the characterization. Since from modal behavior, a fundamental mode of vibration in frequency typically comes with harmonics (other mode of vibrations at integer multiple of the fundamental frequency), once a mode of vibration has been identified for modal characterization, using the method described above for example, its harmonics can be considered as good candidates for generating an excitation signal to improve the resolution of the characterization. Based on the dynamic response of the elongated medium for a selected mode of vibration, as described above, a natural frequency associated with such mode of vibration of the elongated medium can be determined. From that natural frequency, associated harmonics can be identified.

[0101] In an embodiment, the iterative process of excitation of the elongated medium described above can be repeated using a frequency associated with a first one of the harmonics identified. The same process can then be repeated with the frequency associated with a second one of the harmonics, a third one of the harmonics, a fourth one of the harmonics, and so on. In some cases, the elongated medium may have structural limitations, such as damping, attenuation, pipe diameter, material, structural integrity, etc. that affect the capacity of high frequencies to propagate over large distances. Thus, in some applications, such as for a plastic pipe or a PCCP where acoustic waves of high frequency may have limited propagation, it may be preferable to iteratively scan for higher harmonics one harmonic at a time, from lower harmonics towards higher harmonics. In other applications, such as for a metallic pipe where acoustic waves of much higher frequency are able to propagate, the process can be accelerated by targeting the highest possible harmonic(s) that can be detectable at the output locations. Higher frequencywould mean higher resolution, and thus higher precision in the location of the detected anomaly.

[0102] For each excitation of the elongated medium targeting an individual harmonic frequency, the dynamic responses of the elongated medium for the selected mode of vibration, and the harmonics of such mode of vibrations, can be computed. A deviation in indicators such as eigenfrequencies can be analyzed and compared to assess the structural condition of the elongated medium, as described above. By combining the detection of a deviation of frequency of the mode of vibration and that of its harmonics as part of the process to assess the structural condition of the elongated medium, a higher confidence in the results in terms of localized degradation of the elongated medium may be obtained both in terms of absolute level of degradation for a given resolution and accuracy in localizing such defects.

[0103] In at least some embodiments such method of excitations and dynamic characterization of the elongated medium at the selected mode of vibration, including the modes of vibrations corresponding to its harmonics, can be combined with a convergence algorithm. In some embodiments, for example, the convergence algorithm may include a process for identifying modes in a response signal, a process for identifying different harmonics for each identified mode and / or a process for identifying which modes can be used together and which modes need to be considered separately. The convergence algorithm may ensure that the same information about the elongated medium, e.g. stiffness profile or wall thickness profile, is extracted from the use of the fundamental modes and the harmonics. For example, a stiffness profile of degradation variation could be generated for a pipe segment using a fundamental mode A with the associated resolution of this mode A. Using an harmonic of mode A, for example the second harmonic A2 of mode A would allow to characterize the stiffness profile similarly to how the profile would have been generated with mode A but with a higher resolution since the second harmonic A2, as an harmonic mode, would be higher in frequency. The convergence algorithm may ensure that these two modes can be grouped for analysis, that the information as deliverables for this segment, in this case stiffness profile, is converging using these two modes, and that mode A2 provides a similar profile than with the use of mode A but with a higher resolution. The convergence algorithm may provide both an increased level of confidence in the output deliverables and the best possible achievable resolution, converging not only to the absolute value of stiffness for the profile but also tothe more precise locations of detected defects due to the increased resolution.

[0104] In order to locate, spatially, the defect associated with a deviation of resonant frequency, between the input location and output location, a time-windowing can be used on the deconvoluted dynamic response. As such, the dynamic response may be separated into a plurality of time windows, each being representative of a portion of a length of the elongated medium between the input location and the output location. In other words, the dynamic response provided in the frequency domain is transformed, using suited algorithm, e.g. Fourier transform functions, into the time domain and is thereafter discretized into a plurality of time windows. The duration (or length in the time domain) of the time windows is generally chosen so that the length of the time window has a length corresponding to a wavelength of the vibro-acoustic signal. The duration of the time windows may be selected to match one or more wavelengths of the vibro-acoustic-wave signals. For example time windows with different duration could be used, depending on the series of measurements, processing / post-processing iteration, as some possibilities. After being separated, a given frequency bandwidth of each time window may be averaged in order to obtain a dynamic response value, such as the root-mean-square (RMS) value or another value representative of a mean or average value over the time window, varying as a function of the position along the elongated medium. From such value, a stiffness profile of the elongated medium may be computed, based on the variation of the dynamic response value as a function of the position along the elongated medium, for example by solving a mathematical vibro-acoustic model of the elongated medium.

[0105] In at least some embodiments, the methods described above can be implemented as part of a data acquisition system capable of acquiring, and automatically collecting data on the field to conduct dynamic responses analyses of the elongated medium on a per mode of vibration basis. Such data acquisition system can be as the system 100, 300, 400 described herein. In an embodiment, the data acquisition system includes at least one vibration generator as the vibration generators 104, 304, 404 described herein, and at least one sensing unit 200 (200a, b,c, d,e,f,g,h,l ,j).

[0106] Using a vibration generator 104 as described herein coupled to the elongated medium at an input location, and a sensing unit 200 having a sensor 202 (as described herein) coupled to the elongated medium at an output location, a first generic excitation signal could be generated to propagate into the elongated medium and a response to thatexcitation measured at the output location. Such first generic excitation signal and measurement can then be used to dynamically characterize the elongated medium, between the input location and the output location. The dynamic characterization of the elongated medium may include identifying / estimating a modal behavior of the elongated medium, including one or more resonant frequencies and their respective harmonics, using the vibration generator, the sensing unit coupled to the elongated medium, and processing to implement the methods as described herein. In an embodiment, the vibration generator and / or the sensing unit, may be equipped with integrated processing to identify the modes of vibration in the frequency domain of the elongated medium, between the input location and the output location. Once the modes of vibration are identified / estimated (e.g., within a confidence interval or margin of error of ± 10Hz, ± 20 Hz, or ± 30Hz) e.g., through processing of the acquired data obtained from the excitation of the elongated medium by the vibration generator and output signal measured with the sensing unit, the vibration generator may be controlled to excite the elongated medium with the corresponding resonant frequency, or frequency band selected according to the methods described herein, of a selected one of the modes of vibration identified (e.g., via a feedback loop or other similar control logic). Iteration loops to refine the excitation signal based on the methods described herein can be implemented to iteratively excite the elongated medium, measure the response of the elongated medium from such excitation, re-estimate the resonant frequency(ies) of the elongated medium from such iterated excitation loop, and so on, until a desired level of precision / accuracy is obtained. A final, refined, excitation signal can then be used to record measurements at the sensing unit (or more than one sensing unit, such as two of them) along the elongated medium, to provide a basis for the structural condition assessment of the elongated medium. In at least some cases, the vibration generator may be similarly controlled and operated to excite the elongated medium with an input signal having a frequency corresponding to one harmonic frequency of the resonant frequency of the selected one of the modes of vibration identified. The recorded measurements at the sensing unit(s) from such excitation may also form a basis, e.g., together with the other recorded measurements described above, for the structural condition assessment of the elongated medium, through post-processing.

[0107] The data acquisition system may thus collect all the data necessary for a single mode of vibration analysis, including the harmonics of the resonant frequency of such mode. In addition, the data acquisition system may similarly collect data sequentially for each mode of vibration identified, until the data for analyzing the response of a plurality of(or all) individual modes of vibrations of interest have been recorded, on a per mode of vibration basis. Such data can be stored on a memory for immediate or future postprocessing and analyses, to assess the structural condition of the elongated medium (or subcomponent thereof) using the methods described above.

[0108] Fig. 6 is a flow chart of an example of a method 600 for characterizing an elongated medium using a vibration generator and a sensing unit coupled to the elongated medium, and diagnosing the structural condition of such elongated medium, as described herein. The method 600 includes targeting, via vibroacoustic excitation, one or more specific modes of vibration of a structure and determining the structural condition (‘health’) thereof through comparative modal analysis of the measured responses, between them or compared with that of a digital twin, as described herein. The method 600 starts at step 602.

[0109] At step 604, a vibro-acoustic signal is provided at an input location along the elongated medium to propagate into the elongated medium and vibroacoustically excite it. The vibro-acoustic signal may be built based on parameters generated by or received at the vibration generator. The vibro-acoustic signal may be a signal built by a computing device 700 (described later). In an embodiment, the vibro-acoustic signal is built based on information derived from a digital twin of the elongated medium, as described herein. The vibro-acoustic signal has a frequency content or band configured to excite a resonant frequency of a single mode of vibration of the elongated medium. In an embodiment, the frequency content of the vibro-acoustic signal includes and / or overlap with a frequency corresponding to a resonant frequency of the elongated medium. In some cases, the vibro-acoustic signal may include a plurality of frequencies corresponding to several resonant frequencies corresponding to a fundamental resonant frequency of the mode of vibration targeted, and one or more of its harmonics. The resonant frequencies of the elongated medium may be predetermined, by a reference model of the elongated medium. The reference model may be an analytical model, referred to herein as a digital twin, of the elongated medium and / or an experimental model thereof. The experimental model may be a model based on measurements made on a structure corresponding to the elongated medium reproduced in a laboratory, or measurements made on the elongated medium itself, while the analytical model is a digital twin generated using modeling algorithms.

[0110] Predetermining or determining the resonant frequency may be by modal analysis of the digital twin, or, in the alternatives and as described above, determined byvibro-acoustically exciting the elongated medium to identify its modes of vibration. In an embodiment, an iterative method to identify the modes of vibration of the elongated medium includes generating iteratively, via the vibration generator, a plurality of vibroacoustic signals at the input location based on the input signal, to propagate into the elongated medium. In at least some embodiments, at least some iterations of vibroacoustic signal may include at least one vi bro-acoustic wave having a respective frequency, frequency band width, and / or frequency content that is different from that of other iterations of vibro-acoustic signals. Upon excitation of the elongated medium with the vibro-acoustic signals, a respective response signal is measured, via the sensing unit, for each one of the plurality of vibro-acoustic signals, iteratively, and the respective response signal is transduced into respective output signals. From the plurality of output signals (or selected one or more of those output signals), a modal analysis can be performed to identify / estimate one or more excited resonant frequencies of the elongated medium by respective vibro-acoustic signals. In at least some embodiments, a vibro-acoustic signal can be generated for exciting a selected one of the resonant frequencies. In an embodiment, it is desirable to generate a vibro-acoustic signal that is configured to excite a single mode of vibration. As described herein, the vibro-acoustic signal may have a frequency band configured to excite the resonant frequency of a single, targeted, mode of vibration, without overlapping with the resonant frequency of another mode of vibration (i.e. , higher or lower mode of vibration, in the frequency domain).

[0111] At step 606, a response signal representative of a dynamic response of the elongated medium to the vibro-acoustic signal is measured and transduced into an output signal via the sensing unit. The response signal representative of the dynamic response of the elongated medium may include a resonance induced in the elongated medium from the excitation by the vibro-acoustic signal. The output signal can be thereafter processed by a computing device.

[0112] At step 608, a mode of vibration and its modal behavior (e.g., modal shape and resonant frequency) is determined from the processing of the output signal.

[0113] At step 610, a deviation between the resonant frequency of the mode of vibration determined from the output signal and a resonant frequency for that same mode of vibration determined via a model (the predetermined resonant frequency discussed above) is identified / revealed. The deviation in frequency may be visualized (e.g., user interface 108, 308, 408) and / or computed. As detailed above, a deviation in frequencybetween the predetermined frequency resonance and the resonant frequency of the mode of vibration obtained from processing of the output signal can provide information on the structural condition of the elongated medium. In at least some embodiments, a deviation in frequency towards lower frequencies may be indicative of a degradation / failure of the elongated medium, such as a wall thickness reduction of the elongated medium.

[0114] At step 612, information on the deviation in frequency may be conveyed or used to estimate a degradation level of the wall of the elongated medium, and reporting. Preventive actions may then be taken to repair, replace, or investigate a failure / degradation revealed by that information. For example, information on the deviation in frequency and / or estimated degradation level derived therefrom may prompt an alert to act (e.g., start a workflow, maintenance planning, etc.).

[0115] In at least some embodiments, selecting the frequency or frequency band of the vibro-acoustic signal to propagate in the elongated medium may be based on a subcomponent of the elongated medium of interest. As mentioned above, each subcomponent may have respective modes of vibration. Selecting the frequency or frequency band of the vibro-acoustic signal to propagate in the elongated medium may thus allow targeting an excitation of the mode(s) of vibration of a selected subcomponent of the elongated medium. The structural condition of a selected subcomponent based on a targeted excitation of its mode(s) of vibration in the output signal and analysis of the signal response may thus be assessed.

[0116] In some cases, it may be desirable to obtain the dynamic response of the elongated medium based on an excitation of a mode of vibration associated with the coupling of subcomponents of the elongated medium (e.g., coupled layers of the PCCP 540). This may assist in determining the structural condition of one or more other subcomponents of the PCCP, e.g., wiring layer 548, by the use of certain algorithms, as discussed above. In other words, the structural condition of one or more subcomponents of the elongated medium may be derived from the analysis of the dynamic response of the elongated medium based on an excitation of one or more mode(s) of vibration associated with other ones or more subcomponents of the elongated medium. As mentioned above, when evaluating the structural condition of a complex structure, it may be possible to evaluate the structural condition of a selected subcomponent by subtracting the dynamic response of the non-selected subcomponents in the overall dynamic response.

[0117] Part or all the embodiments of the devices, systems and methods described herein may be implemented in a combination of both hardware and software. Fig. 7 illustrates an example of computing device 700 which may be used to implement the method 600 of Fig. 6. The computing device 700 may correspond to the computing device 106 described above (or vice versa). The computing device 700 comprises a processing unit 702 and a memory 704 which has stored therein computer-executable instructions 706. The processing unit 702 may comprise any suitable devices configured to implement the functionality of the sensing system 100,300,400 and / or the method 600 such that instructions 706, when executed by the computing device 700 or other programmable apparatus, may cause the functions / acts / steps performed by the sensing system 100,300,400 and / or the method 600 as described herein to be executed. The processing unit 702 may comprise, for example, any type of general-purpose microprocessor or microcontroller, a digital signal processing (DSP) processor, a central processing unit (CPU), an integrated circuit, a field programmable gate array (FPGA), a reconfigurable processor, other suitably programmed or programmable logic circuits, custom-designed analog and / or digital circuits, or any combination thereof.

[0118] The memory 704 may comprise any suitable known or other machine-readable storage medium. The memory 704 may comprise non-transitory computer readable storage medium, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, semiconductor system, apparatus, or device, or any suitable combination of the foregoing. The memory 704 may include a suitable combination of any type of computer memory that is located either internally or externally to device, for example random-access memory (RAM), read-only memory (ROM), compact disc readonly memory (CDROM), electro-optical memory, magneto-optical memory, erasable programmable read-only memory (EPROM), and electrically-erasable programmable read-only memory (EEPROM), Ferroelectric RAM (FRAM) or the like. Memory 704 may comprise any storage means (e.g., devices) suitable for retrievably storing machine-readable instructions 706 executable by processing unit 702.

[0119] The computing device 700 may be any suitable computing device, such as a desktop computer, a laptop computer, a mainframe, a server, a distributed computing system, a portable computing device, a mobile phone, a tablet, or the like. The computing device 700 may be cloud-based. The computing device 700 or part thereof (e.g., processing unit 702, memory 704, and / or instructions 706) can form part of the vibrationgenerator 104, sensing unit 200, or both, or other components forming part of the system 100, 300, 400.

[0120] The above disclosure sets out various aspects of the technology that may be part of several embodiments. It should be understood that combinations and permutations of various aspects can form part of more than one embodiment.

[0121] From the present disclosure, according to various embodiments, a method for diagnosing / evaluating a structural condition of an elongated medium using a vibration generator and a sensing unit coupled to elongated medium can include the generation, via the vibration generator, of a vibro-acoustic signal to propagate into the elongated medium from an input location along the elongated medium, the measurement at an output location along the elongated medium, via the sensing unit, of a response signal representative of a dynamic response of the elongated medium to that vibro-acoustic signal and the transducing of the response signal into an output signal. Computation of the dynamic response of the elongated medium from the output signal can be performed, via a computing device and / or one or components of a data acquisition system, for example. The tracking of a variation of a resonant frequency associated with a single mode of vibration between the input location and the output location can occur. The variation of the resonant frequency may correspond to a variation of the structural condition of the elongated medium between the input location and the output location. The vibro-acoustic signal used therefor has a frequency band configured to excite a single mode of vibration of a plurality of modes of vibration of the elongated medium. The frequency band includes at least a resonant frequency of the single mode of vibration excited. In at least some embodiments, the vibro-acoustic signal can be a vibro-acoustic wave signal.

Claims

WHAT IS CLAIMED IS:

1. A method for diagnosing a structural condition of an elongated medium using a vibration generator and a sensing unit coupled to elongated medium, the method comprising:generating, via the vibration generator, a vibro-acoustic signal to propagate into the elongated medium from an input location along the elongated medium, the vibro-acoustic signal has a frequency band configured to excite a single mode of vibration of a plurality of modes of vibration of the elongated medium, the frequency band overlapping with at least a resonant frequency of the single mode of vibration;measuring at an output location along the elongated medium, via the sensing unit, a response signal representative of a dynamic response of the elongated medium to the vibro-acoustic signal and transducing the response signal into an output signal;computing the dynamic response of the elongated medium from the output signal; andtracking a variation of the resonant frequency of the single mode of vibration between the input location and the output location, the variation of the resonant frequency corresponding to a variation of the structural condition of the elongated medium between the input location and the output location.

2. The method of claim 1, further comprising selecting the frequency band of the vibro-acoustic signal from first, at least:propagating a first vibro-acoustic signal into the elongated medium, the first vibro- acoustic signal configured to excite the plurality of modes of vibration of the elongated medium;measuring at the output location, via the sensing unit, a first response signal representative of a first dynamic response of the elongated medium to the first vibro-acoustic signal and transducing the first response signal into a first output signal;computing the first dynamic response of the elongated medium from the first output signal; andidentifying the resonant frequency of the single mode of vibration at least from the computing of the first dynamic response.

3. The method of claim 2, wherein propagating the first vibro-acoustic signal into the elongated medium includes generating the first vibro-acoustic signal via the vibration generator, the first vibro-acoustic signal having a frequency bandwidth adapted to excite the plurality of modes of vibration of the elongated medium.

4. The method of claim 3, wherein the first vibro-acoustic signal includes a plurality of vibro-acoustic waves each having a frequency corresponding to a respective predetermined resonant frequency of the elongated medium.

5. The method of claim 4, comprising determining the respective predetermined resonant frequencies of the elongated medium from a model of the elongated medium, wherein the model is an analytical and / or experimental model of the elongated medium.

6. The method of claim 4, wherein the respective predetermined resonant frequencies include a predetermined fundamental resonant frequency and harmonics of the predetermined fundamental resonant frequency.

7. The method of claim 5, further comprising generating the model of the elongated medium from properties of the elongated medium.

8. The method of claim 5, wherein determining the respective predetermined resonant frequencies of the elongated medium includes performing a modal analysis of the model.

9. The method of claim 1 , further comprising selecting the frequency band of the vibro-acoustic signal by first:computing an analytical model of the elongated medium from properties of the elongated medium;selecting a single expected mode of vibration from a plurality of expected modes of vibration of the elongated medium obtained from the computing of the analytical model and;propagating a first vi bro-acoustic signal into the elongated medium, the first vibroacoustic signal configured to excite the single expected mode of vibration of the elongated medium, the first vibro-acoustic signal having a frequency band including at least an expected resonant frequency of the single expected mode of vibration.

10. The method of claim 1 , wherein tracking the variation of the resonant frequency of the single mode of vibration between the input location and the output location includes deconvoluting the dynamic response of the elongated medium.

11. The method of claim 10, further including discretizing the deconvoluted dynamic response of the elongated medium into a plurality of time windows.

12. The method of claim 11, further comprising selecting a duration of a time window of the plurality of time windows based on a wavelength of the vibro-acoustic signal.

13. The method of claim 12, further comprising averaging a frequency bandwidth of each time window of the plurality of time windows to obtain a dynamic response value representative of a mean or average value over each time window of the plurality of time windows as a function of a position between the input location and the output location.

14. The method of claim 2, wherein identifying the resonant frequency of the single mode of vibration at least from the computing of the first dynamic response includes:selecting an harmonic frequency of a mode of vibration of the plurality of modes of vibration obtained from the first dynamic response, the resonant frequency of the single mode of vibration being the harmonic frequency.

15. The method of claim 1, further comprising selecting the frequency band of the vibro-acoustic signal by first:generating, via the vibration generator, a first vibro-acoustic signal to propagate into the elongated medium from the input location along the elongated medium, the first vibro-acoustic signal having a first frequency band configured to excite a single mode of vibration of a plurality of modes of vibration of the elongated medium, the first frequency band overlapping at least a predetermined resonant frequency of the single mode of vibration;measuring at the output location along the elongated medium, via the sensing unit, a first response signal representative of a first dynamic response of the elongated medium to the first vi bro-acoustic signal and transducing the first response signal into a first output signal;computing the first dynamic response of the elongated medium from the first output signal; andidentifying a peak frequency value from the first dynamic response within the first frequency band, and selecting a frequency at the peak frequency value as the resonant frequency to be overlapped by the frequency band of the vibro-acoustic signal.

16. The method of claim 1, further comprising selecting the single mode of vibration from the plurality of modes of vibration of the elongated medium based on at least one of:a desired resolution of the dynamic response of the elongated medium;a desired resolution of the tracking of the variation of the resonant frequency between the input location and the output location;a desired resolution of the tracking of the variation of the structural condition of the elongated medium between the input location and the output location; ora dynamic behavior of a subcomponent of the elongated medium.

17. The method of claim 16, comprising obtaining the predetermined resonant frequency of the elongated medium from a digital twin of the elongated medium.

18. The method of claim 17, further comprising generating the digital twin of the elongated medium from properties of the elongated medium.

19. The method of any one of claims 1 to 18, wherein the structural condition of the elongated medium is a wall thickness or wall stiffness of the elongated medium.

20. A data acquisition system for diagnosing a structural condition of an elongated medium, comprising:a vibration generator for exciting the elongated medium with a first vibro-acoustic signal at an input location along the elongated medium;a sensing unit for measuring a response signal representative of a dynamic response of the elongated medium to the first vibro-acoustic signal of the elongated medium at an output location along the elongated medium; anda processing unit configured to execute instructions for:computing the dynamic response of the elongated medium based on an output signal from the sensing unit, the output signal transduced from the response signal measured by the sensing unit,identifying an estimated resonant frequency of a mode of vibration of the elongated medium from the computed dynamic response; andcausing a generation of a second excitation signal, by the vibration generator, to propagate into the elongated medium, the second excitation signal having a frequency band including or overlapping with at least the estimated resonant frequency of the mode of vibration.

Images