Abstract:
The ultrasonic sensor assembly is provided. The assembly includes a first and second flexible sets of transducers wrapped and permanently attached to the pipe at first and second locations, respectively. Each set of transducers includes at least transducers arranged in a row. The first set of transducers is configured to transmit a wave along the pipe. The second set of transducers is configured to receive the wave transmitted along the pipe. The ultrasonic sensor assembly includes a controller operatively connected to the second set of transducers for receiving information about the wave received by the second set of transducers. The controller is configured to analyze the information about the wave received by the second set of transducers to determine the presence of possible defects in the pipe. An associated method is also provided.

Description:
[0001]    The present application is a continuation of U.S. patent application Ser. No. 14/956,423, filed Dec. 2, 2015, which in turn is a continuation of U.S. patent application Ser. No. 13/747,522, filed Jan. 23, 2013, now U.S. Pat. No. 9,228,888, and benefit of priority is claimed from all of said applications and all of said applications are incorporated herein by reference. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    Field of the Invention 
         [0003]    The present invention relates generally to ultrasonic sensor assemblies, and more particularly, to aligning an ultrasonic sensor assembly on a pipe. 
         [0004]    Discussion of the Prior Art 
         [0005]    Ultrasonic sensor assemblies are known and used in many different applications. Ultrasonic sensor assemblies are used, for example, to inspect a pipe and detect/identify at least one characteristic of the pipe, such as corrosion, voids, inclusions, length, thickness, etc. To accurately determine the location of these characteristics of the pipe, a relative position of a first transducer ring with respect to a second transducer ring should be known. In the past, the first transducer ring would be precisely longitudinally aligned with the second transducer ring, such that circumferential locations of transmitters in the first transducer ring would match circumferential locations of receivers in the second transducer ring. Providing precise longitudinal alignment could be difficult and time consuming. Further, alignment tools (e.g., mechanical tools, optical/laser tools, software based tools, etc.) were used to assist in longitudinal alignment. 
         [0006]    Accordingly, it would be beneficial to provide an ultrasonic sensor assembly that allows for the transducer rings to be arbitrarily installed on the pipe. Further, it would be beneficial to provide this arbitrary installation of the transducer rings without the need for alignment tools. 
       BRIEF DESCRIPTION OF THE INVENTION 
       [0007]    The following presents a simplified summary of the invention in order to provide a basic understanding of some example aspects of the invention. This summary is not an extensive overview of the invention. Moreover, this summary is not intended to identify critical elements of the invention nor delineate the scope of the invention. The sole purpose of the summary is to present some concepts of the invention in simplified form as a prelude to the more detailed description that is presented later. 
         [0008]    In accordance with one aspect, an ultrasonic sensor assembly for a pipe is provided. The ultrasonic sensor assembly includes a first set of transducers configured to be attached to the pipe at a first location. The first set of transducers is flexible and configured to wrap at least partially around the pipe matching a shape of the pipe at the first location. The first set of transducers is permanently attached to the pipe. The first set of transducers includes at least transducers arranged in a first row. The first set of transducers is configured to transmit a wave along the pipe. The ultrasonic sensor assembly includes a second set of transducers configured to be attached to the pipe at a second, different location. The second set of transducers is flexible and configured to wrap at least partially around the pipe matching a shape of the pipe at the second location. The second set of transducers is permanently attached to the pipe. The second set of transducers includes at least transducers arranged in a second, different row. The second set of transducers is configured to receive the wave transmitted along the pipe. The ultrasonic sensor assembly includes a controller operatively connected to the second set of transducers for receiving information about the wave received by the second set of transducers. The controller is configured to analyze the information about the wave received by the second set of transducers to determine the presence of possible defects in the pipe. 
         [0009]    In accordance with another aspect, a method of providing an ultrasonic sensor assembly on a pipe is provided. The method includes providing a first set of transducers configured to be attached to the pipe at a first location. The first set of transducers is flexible and the first set of transducers includes at least transducers arranged in a first row. The method includes wrapping the first set of transducers at least partially around the pipe to match a shape of the pipe at the first location. The method includes permanently attaching the first set of transducers to the pipe such that the first set of transducers is configured to transmit a wave along the pipe. The method includes providing a second set of transducers configured to be attached to the pipe at a second, different location. The second set of transducers is flexible and the second set of transducers includes at least transducers arranged in a second row. The method includes wrapping the second set of transducers at least partially around the pipe to match a shape of the pipe at the second location. The method includes permanently attaching the second set of transducers to the pipe such that the second set of transducers is configured to receive the wave transmitted along the pipe. The method includes providing a controller. The method includes operatively connecting the controller to the second set of transducers for receiving information about the wave received by the second set of transducers. The controller is configured to analyze the information about the wave received by the second set of transducers to determine the presence of possible defects in the pipe. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]    The foregoing and other aspects of the present invention will become apparent to those skilled in the art to which the present invention relates upon reading the following description with reference to the accompanying drawings, in which: 
           [0011]      FIG. 1  is a schematic, perspective view of an example ultrasonic sensor assembly being used with a pipe in accordance with an aspect of the present invention; 
           [0012]      FIG. 2  is a schematic, perspective view of the example ultrasonic sensor assembly similar to  FIG. 1  with waves being transmitted from a first transducer ring to a second transducer ring; 
           [0013]      FIG. 3  is an unwrapped planar view of the ultrasonic sensor assembly and the pipe; and 
           [0014]      FIG. 4  is an unwrapped planar view of the ultrasonic sensor assembly similar to  FIG. 3  during a process of determining a relative position of the first transducer ring with respect to the second transducer ring. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0015]    Example embodiment(s) that incorporate one or more aspects of the present invention are described and illustrated in the drawings. These illustrated examples are not intended to be a limitation on the present invention. For example, one or more aspects of the present invention can be utilized in other embodiments and even other types of devices. Moreover, certain terminology is used herein for convenience only and is not to be taken as a limitation on the present invention. Still further, in the drawings, the same reference numerals are employed for designating the same elements. 
         [0016]      FIG. 1  illustrates a perspective view of an example ultrasonic sensor assembly  10  according to one aspect of the invention. In short summary, the ultrasonic sensor assembly  10  includes a controller  20  in operative association with a first transducer ring  30  and a second transducer ring  40 . The first and second transducer rings  30 ,  40  can transmit ultrasonic waves into a pipe  12  for testing the pipe  12 , including sensing and detecting a characteristic (e.g., corrosion, thickness, voids, inclusions, etc.) of the pipe  12 . To provide improved sensing of the pipe  12 , a relative position of the first transducer ring  30  with respect to the second transducer ring  40  is determined based on analyzing one or more waves  50  (see  FIG. 2 , waves schematically represented as arrowheads) received by the second transducer ring  40  from the first transducer ring  30 . 
         [0017]    The pipe  12  is shown to include a tubular pipe having a generally cylindrical shape extending between a first end  14  and an opposing second end  16 . The pipe  12  can include a non-solid body (e.g., hollow body) or may be solid. It is to be appreciated that the pipe  12  is somewhat generically/schematically depicted in  FIGS. 1 and 2  for ease of illustration. Indeed, the pipe  12  is not limited to the pipe extending along a linear axis, and may include bends, undulations, curves, or the like. The pipe  12  has an outer surface  18  forming a generally cylindrical shape. In further examples, the pipe  12  includes other non-cylindrical shapes and sizes. For example, the pipe  12  could have a non-circular cross-sectional shape, such as by having a square or rectangular cross-section. Still further, the pipe  12  may include a tubular shape, conical shape, or the like. The pipe is not limited to pipes, but instead, could include walls, planar or non-planar surfaces, etc. The pipe  12  could be used in a number of applications, including pipeline corrosion monitoring. As such, the pipe  12  shown in  FIG. 1  comprises only one possible example of the pipe. 
         [0018]    Turning to the controller  20 , the controller is somewhat generically/schematically depicted. In general, the controller  20  can include any number of different configurations. In one example, the controller  20  is operatively attached to the first transducer ring  30  and second transducer ring  40  by means of a wire  22 . In further examples, however, the controller  20  could be in wireless communication with the first and second transducer rings  30 ,  40 . The controller  20  can send and receive information (e.g., data, control instructions, etc.) from the first transducer ring  30  through the wire  22  (or wirelessly). This information can be related to characteristics of the pipe  12  (e.g., corrosion, wall thickness, voids, inclusions, etc.), characteristics of the waves  50  transmitted and/or received by the first and second transducer rings  30 ,  40 , or the like. The controller  20  can include circuits, processors, running programs, memories, computers, power supplies, ultrasound contents, or the like. In further examples, the controller  20  includes a user interface, display, and/or other devices for allowing a user to control the ultrasonic sensor assembly  10 . 
         [0019]    Turning now to  FIG. 2 , the ultrasonic sensor assembly  10  includes the first transducer ring  30 . The first transducer ring  30  can include a size and shape that substantially matches a size and shape of the pipe  12 . For example, the first transducer ring  30  can be attached (e.g., temporarily or permanently) to the pipe  12 , such that the first transducer ring  30  wraps around the outer surface  18 . In the shown example, the first transducer ring  30  has a generally circular shape with a diameter that is slightly larger than a diameter of the pipe  12 . As such, the first transducer ring  30  is in contact with the outer surface  18 . Of course, in further examples, the first transducer ring  30  is not limited to having the circular cross-sectional shape, and could include nearly any cross-sectional size and shape that matches the cross-sectional size and shape of the pipe  12 . In another example, the first transducer ring  30  is formed from a flexible material that can be wrapped around the pipe  12 . 
         [0020]    The first transducer ring  30  is shown to be positioned near the first end  14  of the pipe  12 . In further examples, however, the first transducer ring  30  is not so limited to such a position, and could be arranged at nearly any location along the length of the pipe  12 . For example, the first transducer ring  30  could be closer or farther from the first end  14 , adjacent the second end  16 , or the like. 
         [0021]    The first transducer ring  30  includes one or more transmitters  32 . The transmitters  32  are supported (e.g., fixed) to the first transducer ring  30 , such as being supported by a backing material or the like. The transmitters  32  are somewhat generically/schematically shown, as it is to be appreciated that the transmitters  32  include nearly any size, shape, and configuration. The transmitters  32  are provided to extend around the first transducer ring  30  and in contact with the outer surface  18 . The transmitters  32  can be positioned to extend substantially 360° around the outer surface  18  of the pipe  12 . 
         [0022]    The first transducer ring  30  can be provided with any number of transmitters  32 . Further, the transmitters  32  can be arranged to be closer together or farther apart than as shown. In the shown example, the transmitters  32  include a first transmitter  32   a , a second transmitter  32   b , a third transmitter  32   c , and a fourth transmitter  32   d . While only these four transmitters are labeled in  FIG. 2 , it is understood that the first transducer ring  30  is not limited to including the four transmitters. The first transducer ring  30  could likewise include a fifth transmitter, sixth transmitter, etc. Indeed, other transmitters  32  are included within the first transducer ring  30  but are obstructed from view. 
         [0023]    Each of the transmitters  32  is capable of transmitting (e.g., sending, conveying, etc.) one or more of the waves  50 , including a pulse, energy, and/or other impulses, along the pipe  12 . It is to be appreciated that the waves  50  are somewhat generically/schematically depicted as arrows for ease of illustration. The waves  50  can propagate along an inspection region  34  through the pipe  12  from the first transducer ring  30 . In one example, the waves  50  propagate longitudinally along the pipe  12  (e.g., longitudinal guided wave mode). In other examples, the waves  50  include torsional (shear) and flexural modes in addition to the longitudinal mode. The transmitters  32  can transmit a number of different types of waves  50 . In one possible example, the waves  50  are used to detect characteristics within the pipe  12  (e.g., corrosion, thickness, cracks, voids, inclusions, etc.). In another example, the transmitters  32  each transmit non-dispersive guided waves. As is generally known, non-dispersive guided waves have a generally constant velocity traveling through a given medium (e.g., pipe  12  in the shown example) regardless of the presence or absence of corrosion, thickness variations, cracks, or the like. 
         [0024]    The ultrasonic sensor assembly  10  further includes the second transducer ring  40  spaced apart from the first transducer ring  30  along a length of the pipe  12 . The second transducer ring  40  includes a size and shape that substantially matches a size and shape of the pipe  12 . For example, the second transducer ring  40  is attached to the pipe  12  (e.g., temporarily or permanently), such that the second transducer ring  40  wraps around the outer surface  18 . In the shown example, the second transducer ring  40  has a generally circular shape with a diameter that is slightly larger than a diameter of the pipe  12 . As such, the second transducer ring  40  is in contact with the outer surface  18 . Of course, in further examples, the second transducer ring  40  is not limited to having the circular cross-sectional shape, and could include nearly any cross-sectional size and shape that matches the cross-sectional size and shape of the pipe  12 . 
         [0025]    The second transducer ring  40  is shown to be positioned near the second end  16  of the pipe  12 . In further examples, however, the second transducer ring  40  is not so limited to such a position, and could be arranged at nearly any location along the length of the pipe  12 . For example, the second transducer ring  40  could be closer or farther from the second end  16 , adjacent the first end  14 , or the like. Indeed, the positions of the first transducer ring  30  and second transducer ring  40  could be switched, such that the first transducer ring  30  is closer to the second end  16  while the second transducer ring  40  is closer to the first end  14 . 
         [0026]    The second transducer ring  40  includes one or more receivers  42 . The receivers  42  are supported (e.g., fixed) to the second transducer ring  40 , such as being supported by a backing material or the like. The receivers  42  are somewhat generically/schematically shown, as it is to be appreciated that the receivers  42  include nearly any size, shape, and configuration. The receivers  42  are provided to extend around the second transducer ring  40  and in contact with the outer surface  18 . The receivers  42  can be positioned to extend substantially 360° around the outer surface  18  of the pipe  12 . 
         [0027]    The second transducer ring  40  can be provided with any number of receivers  42 . Further, the receivers  42  can be arranged to be closer together or farther apart than as shown. In the shown example, the receivers  42  include a first receiver  42   a , a second receiver  42   b , a third receiver  42   c , and a fourth receiver  42   d . While only these four receivers are labeled in  FIG. 2 , it is understood that the second transducer ring  40  is not limited to including the four receivers. Rather, the second transducer ring  40  could likewise include a fifth receiver, sixth receiver, etc. 
         [0028]    Each of the receivers  42  is capable of receiving the waves  50  (e.g., pulse, energy, other impulses, etc.) from the transmitters  32  of the first transducer ring  30 . In one example, the waves  50  received by the receivers  42  can be inspected, such as with the controller  20 , to detect the characteristics of the pipe  12 . In particular, features of the waves  50  including a time of flight, amplitude, or the like are analyzed to detect the characteristics. To provide more accurate determination of these characteristics, the waves  50  can first be analyzed to detect the relative position of the first transducer ring  30  with respect to a circumferential position of the second transducer ring  40 . 
         [0029]    Turning now to  FIG. 3 , the operation of determining the relative position of the first transducer ring  30  with respect to a circumferential position of the second transducer ring  40  will now be described. In this example, an unwrapped planar view of the ultrasonic sensor assembly  10  is shown for illustrative purposes and to more clearly depict the locations of the transmitters  32   a - 32   d  with respect to the receivers  42   a - 42   d . In particular, the pipe  12 , first transducer ring  30 , and second transducer ring  40  are depicted as being two dimensionally planar in  FIG. 3  for ease of reference. Further, portions of the pipe  12  from the first end  14  to the first transducer ring  30  and from the second transducer ring  40  to the second end  16  are also not shown so as to more clearly depict the transmitters and receivers. However, in operation, the ultrasonic sensor assembly  10  including the pipe  12  will more closely resemble the structure shown in  FIGS. 1 and 2 . 
         [0030]    To determine the relative position of the first transducer ring  30  and second transducer ring  40 , the first transducer ring  30  will initially transmit the waves  50  along the pipe  12  towards the second transducer ring  40 . In particular, the waves  50  are transmitted from one or more of the transmitters  32   a - 32   d . In the shown example, the waves  50  are transmitted from the third transmitter  32   c , however in operation, the waves  50  could similarly be transmitted from the first transmitter  32   a , second transmitter  32   b , fourth transmitter  32   d , and/or other not shown transmitters. 
         [0031]    The third transmitter  32   c  (or other transmitters) can transmit a plurality of the waves  50 , including a first wave  50   a , a second wave  50   b , a third wave  50   c , and a fourth wave  50   d . Of course, in further examples, any number of waves can be transmitted, such as greater than or less than the four waves that are shown. These waves  50   a - 50   d  can be transmitted simultaneously (i.e., multiple waves transmitted at substantially the same time) or sequentially (i.e., each wave successively transmitted after a preceding wave). As such, the waves  50   a - 50   d  represent simultaneous and/or sequential transmission. The waves  50   a - 50   d  will propagate through the pipe  12  from the first transducer ring  30  towards the second transducer ring  40 . 
         [0032]    The waves  50   a - 50   d  transmitted by the third transmitter  32   c  include non-dispersive guided waves. As is generally known, non-dispersive guided waves traveling through the pipe  12  have a substantially constant velocity that is independent of changes in wall thickness of the pipe  12 . Likewise, defects in the pipe  12 , such as corrosion, voids, inclusions, etc., have a minimal or negligible effect on the velocity of the non-dispersive guided waves through the pipe  12 . Accordingly, a time of flight of the waves  50   a - 50   d  from the first transducer ring  30  to the second transducer ring  40  depends primarily on the distance from the transmitter (e.g., third transmitter  32   c  in the shown example) to one of the receivers. The time of flight will therefore be generally independent of changes in wall thickness or defects (e.g., caused by corrosion, voids, inclusions, etc.). 
         [0033]    The waves  50   a - 50   d  transmitted by the third transmitter  32   c  are received by one or more of the receivers  42  of the second transducer ring  40 . In the shown example, the first receiver  42   a  receives the first wave  50   a , the second receiver  42   b  receives the second wave  50   b , the third receiver  42   c  receives the third wave  50   c , and the fourth receiver  42   d  receives the fourth wave  50   d . Determining the relative position is of course not specifically limited to including the four waves, and instead could include the transmission of more or less waves than as shown. Likewise, the waves  50   a - 50   d  are not limited to being transmitted from the third transmitter  32   c , and instead could be transmitted from one or more of the first transmitter  32   a , second transmitter  32   b , fourth transmitter  32   d , or other, not shown transmitters. Further still, the receivers  42   a - 42   d  are not limited to including the four receivers, and could include a greater or smaller number of receivers than as shown. 
         [0034]    Turning now to  FIG. 4 , the operation of determining the relative position of the first transducer ring  30  and second transducer ring  40  will further be described. As shown, the transmitters  32  of the first transducer ring  30  are longitudinally misaligned from the receivers  42  of the second transducer ring  40 . By being longitudinally misaligned, the transmitters  32  are not located at the same circumferential position as the receivers  42  along the outer surface  18  of the pipe  12 . For example, the first receiver  42   a  is offset (i.e., positioned lower in shown example) than the first transmitter  32   a . Likewise, each of the second receiver  42   b , third receiver  42   c , and fourth receiver  42   d  are offset (i.e., positioned lower) than the second transmitter  32   b , third transmitter  32   c , and fourth transmitter  32   d , respectively. Of course, in further examples, the transmitters  32  could include a larger or smaller offset from the receivers  42  than as shown. 
         [0035]    To determine the relative position, an offset distance of the receivers  42  with respect to a longitudinally aligned positioned will be determined. The longitudinally aligned position includes a location that is longitudinally aligned with one of the transmitters (e.g. first to fourth transmitters  32   a - 32   d ) such that an axis from one of the transmitters to the longitudinally aligned position is parallel to a longitudinal axis of the pipe  12 . For example,  FIG. 4  depicts four longitudinally aligned positions (shown generically/schematically with x&#39;s): a first longitudinally aligned position  142   a , a second longitudinally aligned position  142   b , a third longitudinally aligned position  142   c , and a fourth longitudinally aligned position  142   d . Each of these longitudinally aligned positions corresponds to (i.e., is longitudinally aligned with) one of the transmitters. In particular, the first longitudinally aligned position  142   a  is longitudinally aligned with the first transmitter  32   a . The second longitudinally aligned position  142   b  is longitudinally aligned with the second transmitter  32   b . The third longitudinally aligned position  142   c  is longitudinally aligned with the third transmitter  32   c . The fourth longitudinally aligned position  142   d  is longitudinally aligned with the fourth transmitter  32   d . Accordingly, a line from the first transmitter  32   a  to the first longitudinally aligned position  142   a  will be parallel to the longitudinal axis of the pipe  12 . Likewise, a line from each of the second, third, and fourth transmitters  32   b - 32   d  to the second, third, and fourth longitudinally aligned positions  142   b - 142   d , respectively, will also be parallel to the longitudinal axis of the pipe  12 . 
         [0036]    Next, an offset distance, represented as Δd, between each of the longitudinally aligned positions  142   a - 142   d  and each of the receivers  42   a - 42   d  will be determined. A separation distance, represented as d, is defined as a distance separating each of the receivers  42   a - 42   d . For example, the first receiver  42   a  is separated from the second receiver  42   b  by the separation distance d. Likewise, the same separation distance d separates the second receiver  42   b  from the third receiver  42   c , and the third receiver  42   c  from the fourth receiver  42   d . This separation distance d can be readily obtained in any number of ways, such as by measurement, obtaining from a manufacturer of the second transducer ring  40 , etc. In one example, this separation distance d can be the same for the receivers  42  in the second transducer ring  40  as with the transmitters  32  in the first transducer ring  30 . 
         [0037]    To determine the offset distance Δd, a distance from each of the transmitters  32   a - 32   d  to the receivers  42   a - 42   d  will first be determined. In the shown example, the distance from the third transmitter  32   c  to each of the receivers  42   a - 42   d  is determined by analyzing characteristics of the waves  50   a - 50   d , including time of flight, amplitude, etc. Since the waves  50   a - 50   d  include the non-dispersive guided waves that are generally independent of wall thickness, the time of flight for waves  50   a - 50   d  traveling a longer distance will be longer as compared to a time of flight for a shorter distance. Further, the velocity of the waves  50   a - 50   d  is generally known and constant through the pipe  12 . As such, the time of flight of the waves  50   a - 50   d  can be measured, such as by the controller  20 , for each of the receivers  42   a - 42   d . In particular, the time of flight for the first wave  50   a  from the third transmitter  32   c  to the first receiver  42   a  is measured. Likewise, the time of flight for each of the second wave  50   b , third wave  50   c , and fourth wave  50   d  will be measured from the third transmitter  32   c  to the second receiver  42   b , third receiver  42   c , and fourth receiver  42   d , respectively. 
         [0038]    The time of flight of each of the waves  50   a - 50   d  can then be used to calculate the distance between the third transmitter  32   c  and each of the receivers  42   a - 42   d . The velocity for each of the waves  50   a - 50   d  is known (and is generally the same). Accordingly, the time of flight (e.g., seconds, milliseconds, etc.) for each of the waves  50   a - 50   d  multiplied by the velocity (e.g., distance/seconds or milliseconds) will yield the distance from the third transmitter  32   c  to each of the receivers  42   a - 42   d . This distance can be represented in the formula below as  32   c ,  42 . For example, a distance from the third transmitter  32   c  to the first receiver  42   a  is represented as ( 32   c ,  42   a ). Likewise, distances from the third transmitter  32   c  to the second receiver  42   b , third receiver  42   c , and fourth receiver  42   d  are represented as ( 32   c ,  42   b ), ( 32   c ,  42   c ), and ( 32   c ,  42   d ), respectively. 
         [0039]    With the separation distance d and distances between the third transmitter  32   c  and each of the receivers  42   a - 42   d  now known, the relative position of the transmitters  32   a - 32   d  with respect to the receivers  42   a - 42   d  can now be calculated. Initially, a distance from the third transmitter  32   c  to the third longitudinally aligned position  142   c  is shown below. This distance also corresponds to a length of the inspection region  34 : 
         [0000]      32 c, 142 C=L   (1)
 
         [0040]    A formula representing the distance from the third transmitter  32   c  to the third receiver  42   c  is shown below (as  32   c , 42   c ) and is based on the Pythagorean Theorem. Here, Δd represents the offset distance between the third longitudinally aligned position  142   c  and the third receiver  42   c  while L represents the longitudinal distance from the third transmitter  32   c  to the third longitudinally aligned position  142   c:    
         [0000]      32 c, 42 c =√{square root over (Δ d   2   +L   2 )}  (2)
 
         [0041]    Next, a formula representing the distance from the third transmitter  32   c  to the fourth receiver  42   d  is shown below, wherein (d+Δd) represents the offset distance between the third longitudinally aligned position  142   c  and the fourth receiver  42   d . L again represents the longitudinal distance from the third transmitter  32   c  to the third longitudinally aligned position  142   c:    
         [0000]      32 c, 42 d =√{square root over (( d+Δd ) 2   +L   2 )}  (3)
 
         [0042]    A formula representing the distance from the third transmitter  32   c  to the second receiver  42   b  is shown below, wherein (d−Δd) represents the offset distance between the third longitudinally aligned position  142   c  and the second receiver  42   b . L again represents the longitudinal distance from the third transmitter  32   c  to the third longitudinally aligned position  142   c:    
         [0000]      32 c, 42 b =√{square root over (( d−Δd ) 2   +L   2 )}  (4)
 
         [0043]    Using formulas (3) and (4), the offset distance Δd can be determined: 
         [0000]    
       
         
           
             
               
                 
                   
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         [0044]    Next, the longitudinal distance L between the first transducer ring  30  and the second transducer ring  40  can also be determined: 
         [0000]    
       
         
           
             
               
                 
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                               4 
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                               d 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0045]    Accordingly, by initially knowing the separation distance d between each of the receivers  42   a - 42   d  and the time of flight of each of the waves  50   a - 50   d , the offset distance Δd of the receivers  42   a - 42   d  from the longitudinally aligned positions  142   a - 142   d  is determinable. Likewise, the longitudinal distance between the first transducer ring  30  and second transducer ring  40 , designated as longitudinal distance L, can similarly be calculated. 
         [0046]    It is to be appreciated that shown examples and the aforementioned formulas include the waves  50   a - 50   d  propagating only from the third transmitter  32   c . However, the method of determining the relative position of the first transducer ring  30  with respect to a circumferential position of the second transducer ring  40  is not so limited. Rather, in further examples, any of the transmitters  32  (e.g., first transmitter  32   a , second transmitter  32   b , fourth transmitter  32   d , etc.) could be used instead of the third transmitter  32   c . Similarly, the offset distance Δd and longitudinal distance L could be calculated by using greater than or less than the four waves  50 . Further still, the formulas are not limited to using the second receiver  42   b , third receiver  42   c , and fourth receiver  42   d . Instead, the formulas are still effective when using the first receiver  42   a , some or all of the second, third, and fourth receivers  42   b - 42   d , and/or other, not shown receivers. 
         [0047]    By calculating the relative position of the first transducer ring  30  with respect to a circumferential position of the second transducer ring  40 , precise alignment of the transducer rings is no longer needed. Further, alignment tools (e.g., mechanical tools, optical/laser alignment tools, software tools, etc.) may no longer be needed to precisely align the transducer rings. Instead, the first transducer ring  30  and second transducer ring  40  could be attached to the pipe  12 . Once attached, the aforementioned method can quickly and accurately determine the relative positions of the transducer rings. The first transducer ring  30  and second transducer ring  40  can then be used to accurately determine locations of characteristics (e.g., corrosion, thickness, voids, inclusions, etc.) within the pipe  12 . 
         [0048]    In a second example, the relative position of the first transducer ring  30  with respect to the circumferential position of the second transducer ring  40  is determinable with a parameter optimization process. Within the parameter optimization process, one or more of the waves  50  are initially transmitted by the transmitters  32 . As described above, the waves  50  include non-dispersive guided waves that have a generally constant velocity traveling through the pipe  12 . The velocity of the waves  50  is largely independent of pipe thickness variations, presence/absence of corrosion, cracks, etc. In one possible example, the non-dispersive guided waves have a low frequency such that the sensitivity of the velocity of the waves  50  with respect to pipe thickness changes is negligible. 
         [0049]    The waves  50  transmitted from the transmitters  32  of the first transducer ring  30  are received by the receivers  42  at the second transducer ring  40 . As described above, the characteristics of the waves  50  are inspected, such as with the controller  20 , to detect the relative position of the first transducer ring  30  to the second transducer ring  40 . For example, the characteristics of the waves  50  include the time of flight between transmitters  32  of the first transducer ring  30  and the receivers  42  of the second transducer ring  40 . The time of flight for the waves  50  will be measured for some or all of the combinations of transmitters  32  and receivers  42 . For instance, a separate time of flight between the first transmitter  32   a  and each of the receivers  42  (e.g., first receiver  42   a , second receiver  42   b , third receiver  42   c , fourth receiver  42   d , etc.) is measured. Likewise, times of flights for the second transmitter  32   b , third transmitter  32   c , fourth transmitter  32   d  and each of the receivers may also be measured. 
         [0050]    Next, with these measured times of flights, a model will be created that approximates the relative position of the first transducer ring  30  with respect to a position (e.g., circumferential, axial, etc.) of the second transducer ring  40 . The model can be in the form of an equation, formula, or the like, and can incorporate a number of variables in approximating the relative positions of the first transducer ring  30  and second transducer ring  40 . Variables can include, for example, time of flight between individual transmitters and receivers, the pipe diameter, nominal pipe wall thickness, spacing between the first transducer ring  30  and second transducer ring  40 , etc. 
         [0051]    Within this model, an estimated location of the first transducer ring  30  and second transducer ring  40  is determined. This estimated location can be in the form of an XY position of the individual transmitters  32  and receivers  42 , the relative location of the transmitters  32  to the receivers  42 , or the like. Further, the model may include multiple equations, formulas, etc., such as by having an equation/formula for each combination of transmitters  32  and receivers  42 . This equation/formula includes, as a variable, an estimated time of flight between each particular combination of transmitter  32  and receiver  42 . 
         [0052]    Next, parameter optimization is used to optimize the locations of the first transducer ring  30  with respect to the second transducer ring  40  within the model. In particular, the measured time of flights for each of the waves  50  will be compared to the estimated time of flights generated within the model. For example, the model may generate an estimated time of flight of 150 microseconds between one particular combination of transmitter  32  and receiver  42 . In comparison, the measured value of the time of flight between this combination of transmitter  32  and receiver  42  may have been 151 microseconds. As such, an error of 1 microsecond is determined for this particular transmitter/receiver combination. A similar comparison can then be made for each combination of transmitter  32  and receiver  42  (e.g., difference between measured time of flight and model/estimated time of flight). 
         [0053]    Next, a sum of square errors is used to calculate the difference between the model and measured values. This sum of square errors is used to determine how closely the model approximates the actual positions of transmitters  32  with respect to the receivers  42 . For instance, each of the errors (e.g., difference between measured time of flight and model/estimated time of flight) for each combination of transmitters  32  and receivers  42  is determined. These errors are then each squared (i.e., multiplying each error by itself) and added together. This summation will generate a figure of merit that indicates how closely the model matches the measurement with respect to the relative positions of the first transducer ring  30  and second transducer ring  40 . A lower figure of merit indicates that the model more closely matches the measurements (e.g., measured time of flight) than a higher figure of merit. 
         [0054]    By using the parameter optimization process, a relatively accurate determination of the relative positions of the first transducer ring  30  with respect to a position (e.g., circumferential, axial, etc.) position of the second transducer ring  40  is determinable. In particular, a position of the first transducer ring  30  with respect to the second transducer ring  40  is calculated by comparing measured values (e.g., time of flight between transmitters and receivers) with a model of predicted values. 
         [0055]    The invention has been described with reference to the example embodiments described above. Modifications and alterations will occur to others upon a reading and understanding of this specification. Example embodiments incorporating one or more aspects of the invention are intended to include all such modifications and alterations insofar as they come within the scope of the appended claims.