Abstract:
Methods and systems for generating a curve that represents raw data are provided. In one embodiment, the system includes memory for storing a curve generation application program, a user interface, a display device, and a processor. The processor executes the stored curve generation application program and is coupled to the memory, the user interface, and the display device. The executed curve generation application program includes a first component that receives raw data and a second component that allows for the manual or default setting of a base value for defining weight values for each data point of inputted raw data. A third component generates a curve for representing the raw data based on at least a portion of the data points and the set base value. A fourth component outputs the generated curve to the display device.

Description:
FIELD OF THE INVENTION  
       [0001]     This invention relates to data analysis and, more specifically, to filtering and smoothing of data for improving analysis.  
       BACKGROUND OF THE INVENTION  
       [0002]     Analysis of raw test data has required the need for performing filtering and smoothing of the data in order to allow for an effective analysis. Many times, researchers only look for visual evidences of smoothness. For instance, this evidence might be shapes that are generally pleasing to the eye. However, data requirements can be more stringent. For instance, to be useful to a program, a curve must be numerically smooth. This may be a difficult property to attain without solving complicated linear equations.  
         [0003]     In the experimental data context, physical measurements introduce error that can be both random and specific to a domain. Methods to handle error have been shown to be problematic. In many cases, there is a shifting of the data caused by averaging in time. As well, the resulting model has poorly defined derivatives. Due to the problem of obtaining good and smooth data, researchers have been reduced to hand calculations to preserve data integrity. These hand calculations rely on many visual cues. However, they cannot produce the quality of data or derivatives needed to support modeling, such as simulation or dynamic data analysis.  
         [0004]     One common approach to both filtering and smoothing of raw data is to use a sliding window that crosses multiple data points, and to apply one of a variety of schemes to smooth the data. The schemes include linear or non-linear methods. An example linear method would parametrically set the size of the window, thereby controlling the number of coefficients that are used. The main complaint about this method is that it causes a shift in the sampling phase. Another approach applies least-squares analysis on the fit error in order to determine a curve to represent the data. This method is not sensitive to domain constraints, such as the minimal temperature delta that makes sense in the domain, such as for a particular alloy of a metal. There are many other approaches that require knowledge and insight into higher-order mathematics, such as analysis and filtering in frequency space. Such methods presuppose that the researcher knows how to distinguish between noise and signal within the data stream.  
         [0005]     Therefore, there exists a need for an improved data filtering and smoothing process that can be used in a variety of environments, that can appeal to the intuition, and that can provide highly desirable properties of benefit to the researcher.  
       SUMMARY OF THE INVENTION  
       [0006]     The present invention is directed to methods and systems for generating a curve that represents raw data. In one embodiment, the system includes memory for storing a curve generation application program, a user interface, a display device, and a processor. The processor executes the stored curve generation application program and is coupled to the memory, the user interface, and the display device. The executed curve generation application program includes a first component that receives raw data and a second component that allows for the manual or default setting of a base value for defining weight values for each data point of inputted raw data. A third component generates a curve for representing the raw data based on at least a portion of the data points and the set base value. A fourth component outputs the generated curve to the display device.  
         [0007]     In accordance with further aspects of the invention, the base value is information for defining a tube. The information for defining the tube includes a radius value for the tube.  
         [0008]     In accordance with other aspects of the invention, the curve generation application program further includes a fifth component that sets a threshold value for indicating an allowable percentage of data points not used during the generation of the curve. The third component is further based on the set threshold value.  
         [0009]     In accordance with still further aspects of the invention, the third component generates error information relating to how well the generated curve fits with at least a portion of the data points and the fourth component outputs the generated error information to the memory or the display device.  
         [0010]     In accordance with yet other aspects of the invention, the second component sets a base curve and a weight value for each of the data points, determines error values for each of the data points based on the base curve, adjusts the curve based on the determined error values, adjusts the weight values based on the determined error values, determines error values for each of the data points having a weight value greater than a predefined weight value threshold, adjusts the curve based on the error values determined, and repeats adjusting the weight values until a complete state is asserted. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0011]     The preferred and alternative embodiments of the present invention are described in detail below with reference to the following drawings.  
         [0012]      FIG. 1  illustrates an example computer system for performing the processes of the present invention;  
         [0013]      FIGS. 2, 3A , and  3 B illustrate an exemplary process performed by the computer system shown in  FIG. 1  for providing an optimal output curve of received raw data;  
         [0014]      FIG. 4  illustrates a graph of received raw data and a first derivative of the received raw data;  
         [0015]      FIGS. 5-10  illustrate screen shots of a graphical user interface showing an application program that performs the processes of  FIGS. 2, 3A  and  3 B; and  
         [0016]      FIG. 11A -C and  12 A-C provide an examples of applying the present invention to reverse engineering data for purposes of extracting a feature from a cloud of points. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0017]     The present invention relates to apparatus and methods for more effectively analyzing raw data. Many specific details of certain embodiments in the invention are set forth in the following description and in  FIGS. 1-10  to provide a thorough understanding of such embodiments. One skilled in the art, however, will understand that the present invention may have additional embodiments, or that the present invention may be practiced without several of the details described in the following description.  
         [0018]      FIG. 1  illustrates a computer system  20  that includes a processor with associated memory  24 , a display device  28 , and user interface devices such as a keyboard  32  and a mouse  34 . The processor and memory  24  execute an application program for generating an optimized curve and first and second derivative curves of inputted raw data. The generated optimized curve and the first and second derivative curves of the inputted raw data are displayed on the display device  28  for analysis by a user.  
         [0019]     The computer system  20  may be linked directly or indirectly with devices that gather raw data. Devices that gather raw data can be any of a number of different types of devices such as temperature or stress sampling equipment, or any other device that gathers data. Also, the computer system  20  may analyze pre-existing systems in order to allow reverse engineering by performing an analysis of data of the existing system. FIGS.  11 A-C and  12 A-C, described below, provide an example of applying the computer system  20  to reverse engineering data for purposes of extracting a feature from cloud of points.  
         [0020]     The computer system  20  is a general purpose digital computer. It can be appreciated that the computer system  20  may be linked to other computer systems and computer system components across a public or private data network.  
         [0021]      FIGS. 2 and 3  illustrate processes performed by the application program stored and executed by the processor and memory  24  of the computer system  20 . The processes of  FIGS. 2 and 3  receive and analyze raw data and output optimized curves according to the received raw data. Referring to  FIG. 2 , an exemplary process  100  in accordance with an embodiment of the present invention begins by receiving raw data at a block  104 . At a block  106 , a user is prompted to set a tube radius and a percentage of points outside a tube. The set tube radius defines the radius of a cylindrical tube that is used to identify weight values of raw data points relative to a curve. The percentage of points outside of the tube is a threshold value set to limit or identify what percentage of data points can be outside of the defined tube. It can be appreciated that the tube radius and the percentage of data points outside the tube may be automatically set to default values.  
         [0022]     At a block  110 , the application program generates a curve of the raw data based on the tube radius and percentage of data points outside the tube. This step is described in more detail below with reference to  FIGS. 3A and 3B . At a block  112 , the application program generates images of the generated curve, the tube associated with the curve, first and second derivatives of the generated curve, and error reports regarding the generated curve. At a block  114 , the application presents or displays the generated tube, curve, first and second derivative curves, and the reports to a user.  
         [0023]     Referring now to  FIGS. 3A and 3B , a process  200  is shown for generating an optimized curve of the raw data based on the set tube radius and percentage of data points outside the tube (block  110 ,  FIG. 2 ) in accordance with an embodiment of the present invention. At a block  204 , a default curve is provided relative to the first data point and the last data point and weight values are set for each data point of the received raw data. In this embodiment, weight values for data points vary from  0  to  1  and the default setting that occurs at the block  204  is to set the weight values for each data point at  1 , thus meaning that data points are assumed to be within the tube. At a block  206 , the program determines relative error values for each data point based on the provided default curve and the set tube radius. At a block  208 , the program automatically adjusts the default curve based on the determined relative error values. The curve is a non-uniform rational b-spline that includes a plurality of components, such as b-spline coefficients, knots, and parameters (a mapping between the data points and the b-spline coefficients). Due to the high-continuity desired, b-spline coefficients and knots are paired. The b-spline coefficients (knots) of the curve are adjusted based on the relative error values prior to optimization. For each iteration, one knot (with its coefficient) is inserted where it is expected to do the most good for the fit (generally in a region of the most error. This step also provides one more degree of freedom to the optimizer. Within the optimization step (described below), the parameters can change via call-back according to knowledge obtained by movement through the optimization space. Next, at a block  112 , the weight values for each of the data points are adjusted based on the determined relative error values. If a data point is within the tube, the weight value equals 1, otherwise, the weight value is equal to or greater than 0 and less than 1.  
         [0024]     At a decision block  214 , the program determines if the weight value for a data point and is below a threshold value. If it determined that the weight value for a data point is below the threshold value, at a block  218 , the program puts that data point into an outlier stack (i.e., removes the data point from the set of data points used to adjust the curve) and then proceeds to a block  220  to process the next data point. If the weight value for the data point is not below the threshold value, the program proceeds to the next data point, see the block  220 . At a decision block  224 , the program returns to the decision block  214  if not all the data points have been analyzed with regard to their weight value.  
         [0025]     If all the data points have been analyzed as determined by the decision block  224 , the program continues to the decision block  228  ( FIG. 3B ). At the decision block  228 , the program determines if all the data points are within the tube defined by the tube radius and the present curve. If all the data points are within the tube, then the curve accurately describes the raw data, the curve-generating process  200  is complete, and the process  100  continues to the block  112  ( FIG. 2 ). If not all the data points are within the tube at a decision block  228 , then at a block  230 , the program determines if the number of data points in the outlier stack is greater than or equal to the percentage of data points outside of the tube. If the percentage data points in the outlier stack are greater than or equal to the pre-set percentage of data points outside the tube (block  230 ), the curve-generating process  200  ( FIGS. 3A and 3B ) is complete, and the process  100  continues to the block  112  ( FIG. 2 ).  
         [0026]     As further shown in  FIG. 3B , if the determination at block  230  is negative, then at a decision block  232 , the process  200  identifies whether a threshold of acceptable error values has been reached. If it is determined that the sum of all the weight values is less than the threshold amount, then it is apparent that the present curve is not effective for describing the present data points, and the process  200  returns to the block  110  ( FIG. 2 ) for generating a new curve. If at the decision block  232  the weight values are greater than the threshold amount, the process continues to a decision block  234  that determines if a time limit has expired. The decision block  234  keeps the program from performing an infinite loop or just processing data for too long. If the time limit has expired, the program is complete and returns to the block  112  ( FIG. 2 ).  
         [0027]     If a time limit has not expired, the process continues to a decision block  236  that determines if the number of iterations is greater than a threshold amount. In one particular embodiment, an iteration is performed every time the curve and weight values are adjusted, the blocks  208  and  212 . If the number of iterations are greater than the threshold amount, the program is complete and returns to the block  112  ( FIG. 2 ). If the number of iterations is less than the threshold amount, the process continues to a decision block  240  where the program is complete if the user has performed a cancellation operation. Otherwise, the program returns to  FIG. 3A  at a block  244 . At the block  244 , the program determines relative error values for each data point based on the most recently adjusted curve, and then returns to the block  208  where the curve is adjusted based on these newly determined relative error values. It can be appreciated that the decision steps in the process described above may be placed in various order without departing from the spirit and scope of the invention.  
         [0028]     During each iteration of the process  100 , spline knowledge is used to adjust the working elements (coefficients/knots, parameters) of the present curve. For instance, where there is a collection of data points outside the tube that are not identified as outliers, the curve may be partitioned into another segment in order to move that portion of the curve closer to those data points. In certain situations, the program will put all weights back to 1.0 in order to force recalculation.  
         [0029]     For each iteration, an objective function is applied and information about a problem space is used to guide Sparse Optimal Control Software (SOCS). In this case, the problem space uses spline representation. The objective function is stated as: 
 
 fbar =(1.−gamma)* ssq/npt +gamma* f part 
 
 where: 
        ssq=the sum of the squared errors for each point that is in scope,     fpart=smoothness information, and     gamma=a factor that allows ssq to have more weight than fpart (i.e., fit is more important than smoothness).        
 
         [0033]     The call to SOCS is two-way which allows the program to ask for information as it is needed. Sparse techniques allow faster computation in general than do non-sparse techniques. The information given to SOCS allows the loop to hypothesize and test minor modifications at locations on the curve during one iteration. Between iterations, this routine evaluates the curve at each point. The fit information is fed to an Outlier routine, which takes points out of scope or adjusts their weights according to the error analysis. The object function is re-calculated for the next iteration. Next, fbar and fpart are re-adjusted with new curve information. For each point with an error greater than the tube radius, the error is reported.  
         [0034]     In the Outlier routine, the fit information is used to take points out of scope up to the percentage specified by percent outlier. Points can have weights between  0  and  1 . Points with a weight of  1 . 0  are in the tube. Points outside the tube have weights less than  1 . 0  sufficient to influence the solution as if they are in the tube. Once a point is weighted zero, it is out of scope, and it does not influence the solution. The technique used is a form of robust regression.  
         [0035]      FIGS. 4-10  illustrate an example processing of a  200  second interval of raw data associated with the cooling of an aluminum alloy in accordance with an embodiment of the invention. Referring to  FIG. 4 , a graph is shown that illustrates a raw temperature cooling data  300  graphed relative to temperature and time, and a first derivative  304  of the raw temperature cooling data  300  graphed relative to time and cooling rate. The data illustrated in  FIG. 4  may be presented to the user prior to execution of the process  100 .  
         [0036]      FIG. 5  illustrates a screen shot of a user interface of the application program as displayed on the display device  28  ( FIG. 1 ). The user interface includes a variable setting window  320  adjacent to windows  324 - 328  that illustrate various zoomed views of data points of the raw data  300 . In the variable setting window  320 , the user uses the interface device (keyboard  32  or mouse  34 ) or some other user interface device of the computer system  20  to access a modifiable attributes window  332 . The modifiable attributes window  332  allows the user to set a tube radius value and a percent of data points outside the tube value. The modifiable attributes window  332  may include other adjustable attributes, such as number of curve transitions and degree. The number of curve transitions variable is a threshold limit for the number of significant slope transitions that a generated curve would be allowed. Since the result is provided using the b-spline representation, the degree variable allows the researcher to control the order of the related polynomials. The default value of  3  is generally sufficient, however some data handling situations may warrant use of a different value than the cubic default. In the tube zoom view windows  326  and  328 , the data points are identified by the cross hairs and a generated curve  344  is shown.  
         [0037]      FIG. 6  is a screen shot that includes the variable setting window  320 , a curve section viewing window  350 , and two zoomed view windows  352  and  354  of the generated curve  344  and an associated tube  358  and  360 . Curve  344  is the centerline of the tube which is represented by longitudinal lines that are in the same direction as curve  344  and by rib lines (of length 2 times the input radius) that are perpendicular to curve  344 .  FIGS. 7A  and B illustrate a tube  380  generated by the processes  100  ( FIGS. 2 and 3 ). A line  382  connects the data points of the raw data. The section of the tube  380  and the line  382  shown in  FIG. 7B  is a zoom of a section  390  shown in  FIG. 7A . The tube  380  is positioned to include the generated curve (not shown). The display of the line  382  with the tube  380  allow a user to visually determine how well the application program performed in generating the curve.  
         [0038]      FIG. 8  illustrates a screen shot of the window  320 . The window  320  includes a modify attribute value window  400  that allows a user to change any of the attributes within the modifiable attributes window  332 . In this example, the user is changing the tube radius value from 0.15 to 0.10. Adjacent to the window  320  is a display area  324  for displaying at least a section of the raw data.  
         [0039]      FIG. 9  illustrates a graph  410  that presents the results of the process  100 . The graph  410  illustrates an optimized aluminum alloy temperature cooling curve  420  that is the result of aluminum alloy temperature cooling raw data received by the computer system  20 . Also illustrated are first and second derivative curves  422  and  424 , respectively, of the optimized curve  420 .  
         [0040]      FIG. 10  illustrates a screen shot that includes a first window  450  that illustrates the raw data, a second window  452  that illustrates a section the first and second derivative curves of the optimized curve, and the window  320  that includes an error analysis window  458 . The error analysis window  458  presents the fit error rate of the optimized curve for all of the data points, the fit error rate for the optimized curve of the data points that are within the tube, and the fit error rate of just the data points that are outside of the defined tube. The data included in the error analysis window  458  may be presented in various formats to the user on the display device  28  or may be printed on a printing device (not shown).  
         [0041]      FIG. 11  illustrates a reverse engineering example that applies the invention to discover a tube within a massive set of sampled points. Window  500  shows a portion of data obtained through advanced point sampling methods. The view of Window  500  includes millions of points that represent frames, stringers, tubes (to-be-discovered Tube  502 ), wire bundles, and other components from an existing aircraft (length across Window  500  is about 60 inches). Windows  504  and  506  are zooms into one area of Window  500 . Clamp  508  and Tube  512  are common to both views. Tube  512  is a geometric entity that represents the to-be-discovered Tube  502 . The other items in Windows  504  and  506  are points. The points in Window  506  have been decimated to allow for ease of viewing.  
         [0042]      FIG. 12  illustrates the process of finding a seam within the points for the tube using the invention. Window  520  shows the same view as Window  506  and includes the points and the radius tube (Tube  522 ) that surrounds the seam. Window  520  is a zoom that shows the relationship between the points and Tube  522 . The center line of Tube  522  is the seam of the to-be-discovered Tube  502  (Window  500 ). Clamp  508  is visible in Windows  520  and  524  to show a common reference point. Window  512  shows both the radius tube (Tube  522 ) and the discovered tube (Tube  508 ). The mechanism supported by the invention requires minimal human intervention in terms of defining the scope that is based upon the intuitive concept of a seam.  
         [0043]     While preferred and alternate embodiments of the invention have been illustrated and described, as noted above, many changes can be made without departing from the spirit and scope of the invention. Accordingly, the scope of the invention is not limited by the disclosure of these preferred and alternate embodiments. Instead, the invention should be determined entirely by reference to the claims that follow.