Abstract:
A method of examining a cellular structure includes the steps of providing an inspecting device, a neural network and a target cellular structure that includes a plurality of target cells extending therethrough and further includes a target face exposing an arrangement of the target cells; inspecting the arrangement of cells on the face of the target cellular structure using the inspecting device; representing the arrangement of cells with numerically defined target cell parameters; inputting the target cell parameters into the neural network; and generating an output from the neural network based on the target cell parameters, the output being indicative of a strength of the target cellular structure.

Description:
TECHNICAL FIELD 
       [0001]    The present disclosure relates to neural networks and, more particularly, methods of using a neural network to predict the strength of structures with cells. 
       BACKGROUND 
       [0002]    Honeycomb cellular structures are used in vehicular exhaust systems to reduce pollutants. Such structures are generally formed by extrusion and comprise a network of interconnected web walls that form a matrix of elongated, gas-conducting cells which may be square, octagonal, hexagonal, or the like. In some examples, the network of web walls may be surrounded by a cylindrical outer skin that is integrally connected to the outer edges of the web walls to form a cylindrical structure having opposing inlet and outlet end faces for receiving and expelling exhaust gases through the matrix of cells. 
         [0003]    Honeycomb cellular structures are typically inspected to ensure they meet specifications for cell shape, cell size, web-wall thickness, skin integrity, etc., and to ensure they are free of defects. However, given the large number of cells, it takes a significant amount of time to inspect a single honeycomb cellular structure using inspection methods and systems known in the art. Moreover, the honeycomb cellular structure may be subjected to certain operating conditions under which it must withstand high levels of pressure or force. The pressure that honeycomb cellular structure can withstand is conventionally determined by destroying the structure and results in a wasted part. Moreover, the destroyed honeycomb cellular structure might not correctly predict the strength of a different cellular structure which may have minute structural differences that are hard to observe. Therefore, a need exists for a method and an apparatus that can quickly perform inspection on a ceramic honeycomb structure and predict at the manufacturing stage whether the ceramic honeycomb structure can withstand high levels of pressure or force without destruction of the honeycomb structure. 
       SUMMARY 
       [0004]    In one example aspect, a method of examining a cellular structure includes the steps of providing an inspecting device, a neural network and a target cellular structure that includes a plurality of target cells extending therethrough and further includes a target face exposing an arrangement of the target cells; inspecting the arrangement of cells on the face of the target cellular structure using the inspecting device; representing the arrangement of cells with numerically defined target cell parameters; inputting the target cell parameters into the neural network; and generating an output from the neural network based on the target cell parameters, the output being indicative of a strength of the target cellular structure. 
         [0005]    In one example of the example aspect, a method of examining a cellular structure includes the steps of: providing an inspecting device, a storage medium, a plurality of sample cellular structures and a neural network, each of the sample cellular structures including a plurality of sample cells extending therethrough and further including a sample face exposing an arrangement of the sample cells; inspecting the arrangement of sample cells on the sample face of each of the sample cellular structures using the inspecting device; representing the arrangement of sample cells of each of the sample cellular structures with numerically defined sample cell parameters; applying force on each the sample cellular structures while measuring a sample strength parameter representing a maximum force the sample cellular structure can endure prior to destruction; storing in the storage medium the sample cell parameters and the sample strength parameter corresponding to each of the sample cellular structures so as to obtain a sample database; and inputting the sample cell parameters and the sample strength parameter stored in the storage medium into the neural network such that the neural network can detect a relationship between the sample strength parameter and the sample cell parameters based on the sample database. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0006]    These and other aspects are better understood when the following detailed description is read with reference to the accompanying drawings, in which: 
           [0007]      FIG. 1  is a schematic view of an example embodiment of a system configured to examine a cellular structure; 
           [0008]      FIG. 2  is a first image of a face of the cellular structure which is captured by the system and in which cells are detected at every first interval; 
           [0009]      FIG. 3  is a second image of the face of the cellular structure which is captured by the system and in which the cells are detected at every second interval; 
           [0010]      FIG. 4  is a close up view of a cell in an image of the face of the cellular structure captured by the system; 
           [0011]      FIG. 5  is a schematic representation of an operation of an example embodiment of a neural network; 
           [0012]      FIG. 6  is a flow chart representing multiple operating steps during a learning mode of the system; 
           [0013]      FIG. 7  is a flow chart representing multiple operating steps during a predicting mode of the system; and 
           [0014]      FIG. 8  is a flow chart representing multiple operating steps during a correcting mode of the system. 
       
    
    
     DETAILED DESCRIPTION 
       [0015]    Examples will now be described more fully hereinafter with reference to the accompanying drawings in which example embodiments are shown. Whenever possible, the same reference numerals are used throughout the drawings to refer to the same or like parts. However, aspects may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. 
         [0016]    Example embodiments of apparatus and methods of examining a cellular structure are provided. Cellular structures can comprise various cellular structure configurations for different applications. For example, the cellular structures can comprise honeycomb cellular structures for vehicular exhaust applications. For instance, the cellular structure can comprise a ceramic honeycomb substrate that can be used to receive a washcoat of a catalytic agent to reduce hydrocarbon emissions in a vehicular exhaust system. In addition or alternatively, the ceramic honeycomb substrate may comprise porous walls to allow the honeycomb cellular structure to remove particulates from the vehicle exhaust stream. 
         [0017]    As shown in  FIG. 1 , an example embodiment of a system  10  configured to examine a cellular structure  12  is shown. The system  10  may include a conveyor  14 , an inspecting device  16  and a processing device  18  (e.g., a computer). The cellular structures  12  may be made of moldable material such as ceramic and may be manufactured through a variety of methods including an extrusion process. The cellular structures  12  may include a plurality of cells  12   b  ( FIG. 4 ) that extend therethrough and may include a face  12   a  that may be located at an end and exposes an arrangement of the cells. The cellular structures  12  may be placed on the conveyor  14  with the face  12   a  oriented toward the inspecting device  16 . The conveyor  14  may transport a plurality of cellular structures  12  along a belt such that each cellular structure  12  passes underneath the inspecting device  16  and each cellular structure  12  may come to a stop when located directly under the inspecting device  16 . 
         [0018]    The inspecting device  16  may include a lens  20 , a charge-coupled device (CCD) camera  22  and an illuminator  24 . The lens  20  may be configured to magnify the face  12   a  of the cellular structure  12  for close-up inspection of the arrangement of the cells  12   b  while the illuminator  24  may be configured to flash light as an image of the face  12   a  is taken by the CCD camera  22 . The CCD camera  22  may scan the face  12   a  of the cellular structures  12  by taking composite line images of the face  12   a.  The inspecting device  16  thereafter transmits the image of the face  12   a  to the processing device  18  which may include a storage medium  26  where the image may be stored and/or processed and a neural network  28 . 
         [0019]    In one set of example operations, the processing device  18  may signal the illuminator  24  to strobe light onto the face  12   a  of the cellular structure  12  thereby freezing the motion of the cellular structure  12  that is moving on the conveyor  14 . The CCD camera  22  captures an image which is transmitted to the storage medium  26 . The processing device  18  may analyze every cell in the image generating a vector of measurements and may organize the information about each cell into rows and columns. 
         [0020]    The processing device  18  can detect and indicate the locations of the cells  12   b  with a set of Cartesian coordinates. The processing device  18  may be configured to detect every nth cell spaced apart at regular intervals along rows and columns rather than every single cell on the face  12   a  of the cellular structure  12 . Information relating to every single cell on the face  12   a  may be more than necessary and may cause delay of operations. For example,  FIG. 2  shows every tenth cell along rows and columns as measured from an origin (i.e., (0,0)), located at the center of the face  12   a,  and  FIG. 3  shows every twentieth cell along rows and columns as measured from the origin. The density of the cells that are detected by the processing device  18  may change depending on the amount of information that will be provided to the neural network  28 . Based on a comparison between the actual locations of the cells  12   b  (see  FIG. 4 ) relative to the origin and the optimal locations of the cells  12   b  relative the origin, it is possible to determine the deviations and distortions in the arrangement of the cells  12   b.    
         [0021]    Moreover, as shown in  FIG. 4 , there are other cell parameters that the processing device  18  can detect through a close-up inspection of the image of the face  12   a  such as cell corner angles (e.g., upper left angle (ULA)), cell pitches (e.g., horizontal cell pitch (HCP) or vertical cell pitch (VCP)), wall thicknesses (e.g., vertical wall thickness (VWT) or horizontal wall thickness (HWT)), and wall bows (e.g., horizontal wall bow (HWB) or vertical wall bow (VWB)). Further details relating to the inspecting device  16  and cell parameters obtained using the inspecting device  16  are described in application Ser. No. 12/617,778, filed Nov. 13, 2009, which is incorporated herein by reference in its entirety. 
         [0022]    With regard to cell corner angles, while information concerning all four of the cell angles is available, only one cell angle per cell is needed to characterize the angular information for a given cell. Note that square cell  12   b  contains four angles so that all of the angles must add up to 360 degrees. Typically, the angles at the opposite corners of cell  12   b  are equal and the other two angles are approximate complementary angles, thereby allowing for just one cell angle for cell characterization. Horizontal cell pitch or HCP generally measures the difference in the X-coordinates of cell corners. While each cell  12   b  includes two such cell pitches (upper and lower), only one such measurement is needed for most applications. In an example embodiment, an average of the upper and lower horizontal cell pitch HCP is used. Note also that the bottom HCP is the same as the top HCP of the cell directly below so that no information is lost. Vertical cell pitch generally measures the difference in the Y-coordinates of cell corners. As is the case with the horizontal cell pitch HCP, while each cell includes two vertical cell pitches (upper and lower), only one such measurement is needed for most applications. In an example embodiment, an average of the left and right vertical cell pitch VCP is used. Note also that the right VCP is the same as the left HCP of the cell directly to the right so that no information is lost. Horizontal wall thickness or HWT measures the location of the top and bottom edges of the top horizontal web wall and subtracting the two locations. An example of this calculation is carried out for each set of 5 μm pixels that compose the top and bottom edges of web wall. Once the differences are calculated (this may produce between 100 and 300 thickness measurements, depending on the size of cell  12   b ), they are averaged to produce an average thickness. Vertical wall thickness or VWT is calculated in an analogous manner to the horizontal wall thickness HWT. Horizontal wall bow or HWB measures the center point of the top horizontal web wall. This center point is defined as the midway point between the two top corners of the cell  12   b  and the midway point of the top of the web wall and the bottom of the web wall at the location of the midway point. A second point is found by drawing a line between the two top corner points of the cell and finding the center point of this line. The horizontal wall bow is the difference in the X-direction between these two points. The web wall can bow into the cell or away from the cell. If the bow projects into the cell its value is negative, and if it projects out from the cell it is positive. The vertical wall bow or VWB is calculated in an analogous manner to the horizontal wall bow. Another perimeter detected by the processing device  18  may include a perimeter or outer skin of the face  12   a  which can be defined by a best-fit shape (e.g., a circle, an oval, etc.) and which can be used to find a geometric center of the face  12   a.  A shape vector may define in polar coordinates the deviation from the actual perimeter shape to the best-fit perimeter shape. Yet another perimeter detected may be the thickness of the outer skin of the face  12   a.  A thickness may be defined by measuring the variation in skin thickness by subtracting from the outer skin radius the inner skin radius at various angles around the skin. 
         [0023]    In order to determine the parameters indicated on  FIG. 4 , it may be necessary to first find the center of the face  12   a  based on the best-fit perimeter shape and then find best-first vertical and horizontal centerlines that form an idealized or reference web including the best-fit web intersections corresponding to corners of an idealized cell  12   b.    
         [0024]    Moreover, in certain cases to be discussed below, another cell parameter that is indicative of an isostatic strength of the cellular structure  12  can be measured. In one example setting to measure the isostatic strength of a cellular structure  12 , the cellular structure  12  can be submerged in a liquid and the pressure of the liquid can be gradually increased until the cellular structure  12  cannot withstand the pressure and is destroyed such as by cracking or imploding. The maximum pressure or force endured by the cellular structure  12  can be measured and used as a strength parameter of the cellular structure  12 . 
         [0025]    All of these cell parameters can be defined numerically such that one set of numerical values corresponding to the aforementioned cell parameters can be obtained after scanning the face  12   a  of each cellular structure  12 . Moreover, the numeral values corresponding to the cell parameters can be stored in the storage medium  26 . 
         [0026]    As shown in  FIG. 5 , the neural network  28  of the processing device  18  may process information through an interconnected group of artificial neurons  30 . An example embodiment of the neural network  28  is shown schematically in  FIG. 5  and has three layers  32   a,    32   b,    32   c  of neurons  30 . The first layer  32   a  has input neurons  30   a  that send information by way of synapses  34  to the second layer  32   b  of neurons  30  and then to the third layer  32   c  of output neurons  30   b.  Manipulation of the information occurs by altering weights which are parameters stored at the synapses  34 . The neural network  28  has the capability to learn such that, if given a specific task to solve and a class of functions, the neural network  28  is able to solve the task in some optimal sense by observing the information transmitted through the neurons  30 . 
         [0027]    Referring to  FIG. 6 , the aforementioned learning capability of the neural network  28  can be put to use by configuring the system  10  into a learning mode in which the neural network  28  detects or hypothesizes a relationship between the strength parameter and the cell parameters. In an example embodiment, the face  12   a  of a sample cellular structure  12  is captured as an image or scanned by the inspecting device  16  (step L 1 ) and is turned into a set of numerical values representing the sample cell parameters (step L 2 ). Then, the strength of the sample cellular structure  12  is measured during the above-mentioned destruction process and is represented as the sample strength parameter (step L 3 ). The cell parameters and the strength parameters obtained from the sample cellular structure  12  are stored in storage medium  26  (step L 4 ) and are input into the neural network  28  (step L 5 ). The neural network  28  hypothesizes a relationship between the strength parameter and the cell parameters by observing the values of the strength parameter and the cell parameters obtained from the sample cellular structure  12  (step L 6 ). Thereafter, these steps are repeated so that the neural network  28  can observe the values in a sample database containing the strength parameter and the cell parameters obtained from a plurality of sample cellular structures  12 . The sample database may be formed from cell parameters and strength parameters obtained from a large pool of sample cellular structures. The relationship detected by the neural network  28  is likely to be more reliable with a larger the pool of sample cellular structures  12 . It may be possible to first form a sample database by gathering the cell parameters and the strength parameters from the pool of sample cellular structures  12  and provide the parameters to the neural network  28  at once. 
         [0028]    The neural network  28  may determine, for example, that a few of the aforementioned cell parameters play predominant roles in deciding the strength parameter of the cellular structure  12  and that the strength parameter is proportional to each of these cell parameters. The neural network  28  may generate multiple neural net models each of which has a different set of weights for each of the synapses in the neural net model. Out of the multiple neural net models, the neural net model with the best accuracy can be generated as a program in C code which can then be used to predict the isostatic strength of the cellular structures  12 . 
         [0029]    However, due to the unclear nature of neural networks  28 , which imitate the functioning of the neurons in the human brain, it may not be possible to unambiguously express the relationship detected by the neural network  28  in mathematical terms, algorithmic terms, or other terms of notations commonly used in other fields of art. Thus, the terms “hypothesize” or “detect”, which are used to describe the function of the neural network  28  recognizing a relationship between the strength parameter and the cell parameters, should not be construed to necessarily mean that the relationship is definable without uncertainty, that the relationship is expressible with notations commonly used in various fields of art or that the relationship is perceptible by the human brain. 
         [0030]    A person of ordinary skill in the art will understand and recognize that some lack of clarity is unavoidable in using a neural network  28  but that the capabilities of the neural network  28  can still be put to use despite a failure to completely understand how the neural network  28  determined the relationship or obtained an output. Thus, despite the unclear nature of the relationship, the relationship detected by the neural network  28  may be used to yield an output value that can be used to determine whether or not the cellular structure  12  is suitable for use in a given environment (e.g., vehicular exhaust systems). While the output value may be a numerical prediction of the strength of the target cellular structure  12 , the output value may also be expressed in terms of “pass” or “fail” indicating whether or not the cellular structure  12  can endure the pressures or forces in a given set of operation conditions. 
         [0031]    Moreover, after the neural network  28  has detected a relationship between the strength parameter and the cell parameters, the system  10  can be configured into a predicting mode in which the strength of a target cellular structure  12  is predicted after inspecting the face  12   a  of the cellular structure  12  as shown in  FIG. 7 . In an example embodiment, the face  12   a  of the target cellular structure  12  is scanned using the inspecting device  16  (step O 1 ) and the target cell parameters are represented in numerical values (step O 2 ). Then, the target cell parameters are input into the neural network  28  (step O 3 ) and the neural network  28  yields an output value corresponding to the target cellular structure  12  based on the cell parameters obtained by scanning the face  12   a  (step O 4 ). 
         [0032]    A cellular structure  12  provided to help the neural network  28  detect the relationship during the learning mode can be characterized as a ‘sample’ cellular structure  12  that is used as a dummy while a cellular structure  12  the strength of which the neural network  28  attempts to predict during the predicting mode can be characterized as a ‘target’ cellular structure  12 . Moreover, the features of the cellular structure  12 , such as the face  12   a , the cells  12   b  or the parameters, can also be characterized as ‘sample’ or ‘target’ in the same manner. 
         [0033]    Furthermore, the system  10  may also include a correcting mode ( FIG. 8 ) in which, after the neural network  28  has detected a relationship between the strength parameter and the cell parameters based on the sample database, the neural network  28  verifies a reliability of the relationship using a pool of target cellular structures  12 . In an example embodiment, the inspecting device  16  scans the face  12   a  of a target cellular structure  12  (step C 1 ) and represents the target cell parameters with numerical values (step C 2 ). The target cell parameters are input into the neural network  28  (step C 3 ) and the neural network  28  yields an output value based on the target cell parameters (step C 4 ). The strength parameter of the target cellular structure  12  is then measured using the aforementioned destruction process (step C 5 ) and is input into the neural network  28  (step C 7 ). The neural network  28  verifies whether the output value is a reliable indicator of the strength of the target cellular structure  12  through comparison with the strength parameter and adjusts the relationship correcting any present discrepancy (step C 8 ). For example, the adjustment of the relationship may be conducted by changing the weights stored at the synapses  34  of the neural network  28 . Thereafter, these steps are repeated for a plurality of target cellular structures  12 . It may be possible to first form a target database containing the cell parameters and the strength parameter from a pool of target cellular structures  12  and then to provide the parameters to the neural network  28  for necessary adjustment of the relationship. 
         [0034]    It will be apparent to those skilled in the art that various modifications and variations can be made without departing from the spirit and scope of the claimed invention.