Abstract:
The width of bands to be laminated on a mill train is adjusted by vertical upsetting rollers, resulting, however, in a narrowing at the band ends due to the asymetric material flow there. In order to solve the problem, the upsetting rollers are so designed as to move at the passage of the band ends in keeping with a curve defined according to specified parameters. The parameters are based on neuro-computer made predictions related to the milling process.

Description:
FIELD OF THE INVENTION 
     The present invention relates to a method of optimizing the band width distribution at the end of a band passing through a mill train. 
     BACKGROUND INFORMATION 
     One of the main problems in rolling bands, for example, band steel, is achieving a basic rectangular shape with a width that is constant over the band length. Vertical upsetting rollers are used in the mill train to control the band width. If the upsetting rollers are operated with a constant setting, the band becomes usually narrower at the band ends, i.e., at the band head and the band foot, than in the mid-part due to The asymmetric material flow and other effects. In order to prevent this from occurring, the adjustment position of the upsetting rollers is adjustable during the passage of the band, the adjustment being widened with respect to the mid-part as the band ends pass through in the form of short excursions, also known as short strokes. This adjustment correction at the band head and band foot is performed according to a curve (Short Stroke Control-SSC curve), which can be defined by preset parameters. 
     SUMMARY 
     An object of the present invention is to produce a band width distribution at the band ends as close to the specified one as possible by providing a curve for the adjustment position of the upsetting rollers. 
     In In accordance with the present invention, the parameters for forming the curve according to which the position of the upsetting rollers is adjusted during the passage of the band ends are set on the basis of predictions concerning the rolling process using neural networks, with the prediction being continuously improved by on-line teaching of the neural networks on the rolling process. Preferably separate neural networks are used for the band head and the band foot. For consecutive passes of the same band, i.e., for several passes, separate neural networks may be used. If the number of passes is always the same, a single neural network can be used for determining the parameters of the curve of the upsetting rollers in the consecutive passes. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows an example of the width distribution of a rolled band and a curve derived therefrom for the upsetting rollers to correct the band width distribution to 
     FIG. 2 shows an example of the control structure principle of a mill train having a unit for determining parameters for the definition of the curve to 
     FIGS. 3 through 8 show different examples of implementation of the unit for determining the curve parameters to 
     FIG. 9 shows a detailed diagram for determining the curve parameters based on the example of FIG.  8 . 
    
    
     DETAILED DESCRIPTION 
     The diagram of FIG. 1 shows the exemplary width distribution y of a band over its length l when passing through a mill train having, in addition to horizontal flattening rollers for band thickness control, upsetting rollers for band width control. For constant upsetting roller adjustment, the band width is reduced at the band ends, i.e., at the band head and the band foot, due to asymmetric material flows in the band. In order to counteract this effect and maintain a rectangular band shape, the adjustment position of the upsetting rollers is adjusted as the band ends pass through following a curve f, composed of two straight-line segments in the example shown, which can be set for each pass of the same band and separately for the band head and the band foot. Curve f is described by four parameters in the form of two adjustment correction values a 1  and a 2  and two length coordinates l 1  and l 2 . Adjustment correction values a 1  and a 2  refer to the roller gap, so that the travel of the two upsetting rollers is always one-half of that value. Of course, the curve can also be described in other ways and using more parameters. 
     Parameters a 1 , a 2 , l 1 , and l 2  of curve f are to be determined so that, according to the curve defined by the parameters, an adjustment of the adjustment positions of the upsetting rollers results in a predefined specified band width distribution, which in this case is a rectangular band shape at the band ends. This is accomplished, as is elucidated in the following with reference to several examples, using neural networks, with individual parameters, here, for example, length coordinates l 1  and l 2 , being also predefined as empirical values. 
     FIG. 2 shows the control structure principle of a mill train  3 , in which the actual band width distribution Y actual  of a band  4  passing through mill train  3  is optimized according to a predefined specified band width distribution Y set point . Mill train  3  is a cogging train here, which has one or more horizontal roll stands with flattening rollers  5 , with a vertical roll stand with upsetting rollers  6  being arranged upstream from each of the two last horizontal roll stands and, if needed, from other horizontal stands, here the last two horizontal stands. Before a band  4  enters mill train  3 , relevant process parameters x of the rolling process are precalculated on the basis of specified values SW and primary data PD and using mathematical models  8  of the rolling process in a precalculating unit  7  and uploaded to a base automation unit  9 , which uses these parameters to pre-adjust mill train  3 . During the rolling process, relevant measured quantities of the rolling process are continuously detected using a measured value detection unit  10 . The measured values are supplied to base automation unit  9  to perform control functions and to a recalculator  11 . Recalculation  11  uses the same mathematical models  8  as precalculating unit  7  and adapts the respective model parameters on the basis of the measured quantities representing the actual course of the rolling process. Thus the precalculation is continuously improved and adjusted to the actual process for each subsequent band  4  to be rolled. 
     Basic automation unit  9  contains a suitable control device  12  for controlling the adjustment of upsetting rollers  6 . Control device  12  generates, from parameters s supplied to it, for example, s=(a 1 , a 2 ) according to FIG. 1, a curve f, which is used to adjust the position of upsetting rollers  6  as the band ends pass through. Parameters s for curve f are determined in a unit  13  first as a function of predefined specified band width distribution y set point  and precalculated process parameters x, using at least one neural network  14 , which delivers a prediction on the upset variations at the band end. To improve and adapt the predictions of neural network  14  to the actual process, the actual band width distribution Y actual  is measured at the discharge end of mill train  3  using a width measuring device  15 , and neural network  14  is adjusted using this value and process parameters X nach  recalculated in recalculator  11 . 
     Regarding the number of neural networks  14  used, preferably separate neural networks are used for the band head and the band foot. In addition, separate neural networks may be used for successive passes of the same band  4 . If, however, the number of passes is variable from one band to another the use of separate neural networks for the greater number of passes is disadvantageous, since in that case less training data is obtained. 
     FIGS. 3 and 4 show a first exemplary implementation of unit  13  in two operating states. A neural forward model  140  is used here as a neural network, which mirrors the upset variation in its natural cause/effect relationship. The input parameters of neural network  140  in its training phase (FIG. 3) include the recalculated process parameters X nach  and parameters s actual  of the curve, which are determined from measured curve f actual  using a recalculation unit  16 , according to which upsetting rollers  6  are driven during the rolling process. Neural network  140  delivers a prediction for band width distribution y, which is compared with the measured actual band width distribution y actual . Depending on the error Δy found in this comparison, neural network  140  is adjusted, so that it provides the most accurate possible prediction of band width distribution y achieved for the predefined parameters s of the curve and available process parameters x. 
     FIG. 4 shows how the optimum parameters s opt  of a curve with which a predefined specified band width distribution yset point is achieved are determined. For this purpose, starting values s start  for curve parameters s are first supplied to a computing unit  17  and sent to adapted neural network  140  together with the precalculated process parameters x. Adapted neural network  140  delivers a prediction for band width distribution y, which is compared with specified band width distribution y set point . If the difference between the predicted band width distribution y and specified band width distribution yset point exceeds a predefined limit value, starting values s start  are modified by an absolute value Δs. Using the new parameters s=s start +Δs, neural network  140  delivers a new prediction for band width distribution y, which is again compared with specified bandwidth distribution y set point . Parameters s for the curve are modified by an absolute value Δs stepwise until the difference between predicted band width distribution y and specified band width distribution yset pointno longer exceeds the predefined limit value. 
     Parameters s thus determined correspond to the optimum parameters s opt  sought for the curve, with which the adjustment position of upsetting rollers  6  is controlled. 
     In the exemplary embodiment of unit  13  illustrated in FIGS. 5 and 6, two neural networks  140  and  141  are used, of which the first neural network  140  is a neural forward model as described in FIGS. 3 and 4, and second neural network  141  is a neural backward model describing the inversion of the natural cause/effect relationship. As shown in FIG. 5, in the first operating mode of unit  13 , first neural network  140  is trained in the same manner as described with reference to FIG.  3 . 
     According to FIG. 6, after completion of the training of the first neural network  140 , a prediction of parameters s of the curve is generated by second neural network  141  on the basis of a predefined specified band width distribution yset point and the previously computed process parameters x, according to which upsetting rollers  6  are adjusted during the passage of the band. The resulting measured band width distribution yactualis compared to specified band width distribution y set point ; the error Δy obtained in this comparison is back-propagated by the adapted first neural network  140  and is used for adapting the variable network weights w(NN 141 ) of the second neural network  141  by the gradient method:              ∂   Δ                   y       ∂     w        (     NN   141     )           =           ∂   Δ                   y       ∂   y       ·       ∂   y       ∂   s       ·       ∂   s       ∂     w        (     NN   141     )                                    
     The embodiment shown in FIG. 7 for unit  13  includes a neural backward model  141  as a neural network like the one illustrated in FIGS. 5 and 6. This neural network  141 , when adapted, delivers a prediction of parameters s of the curve as a function of a predefined specified band width distribution yset point the pre-calculated process parameters x according to which the position of upsetting rollers  6  is adjusted during the passage of the band. 
     To adapt neural network  141  to the actual, process, the measured actual band width distribution yactual and the recalculated process parameters X nach  are supplied as inputs to neural network  141 , whose network response s is compared with the actual curve parameters sactual determined from measured curve factual using recalculator  16 . Neural network  141  is adapted depending on the error Δs obtained in this comparison. 
     The embodiment of unit  13  shown in FIG. 8 is based on the fact that in the case of an error in band width distribution, i.e., of a difference Δy between specified band width distribution yset point and the measured actual band width distribution y actual , curve factual for upsetting rollers  6  must be changed by the absolute value of this difference Δy in order to compensate for the error. Therefore a neural backward model can be used as a neural network  142 . Specified band width distribution yset point established once for all, i.e., for a rectangular shape of the band ends, so that neural network  142  has a reduced set of functions compared to the examples described above, and only process parameters x or x nach  are supplied to it as inputs for the prediction of curve parameters s. 
     Upstream from the band feed, neural network  142  delivers a prediction of parameters s of curve f based on pre-calculated process parameters x, on the basis of which upsetting rollers  6  are pre-adjusted. 
     After the passage of the band the desired specified band width distribution yset point is compared with the measured actual band width distribution y actual . The measured curve factual is corrected, using the difference obtained Δy to yield a specified curve fset point, whose respective parameters Sset point are determined using a recalculator  18 . Neural network  142  delivers, on the basis of the recalculated process parameters x nach  supplied to it, a prediction of curve parameters s, which are compared with parameters S set point of the specified curve f set point ; the difference Δs obtained is used for the adaptation of neural network  142 . The recalculation interface between curve f and its parameters s, which in the example shown is recalculator  18 , can of course also be arranged otherwise in that parameters s predicted by neural network  142  are recalculated to yield a predicted curve f and the predicted curve f is compared with specified curve f set point . This results also from the following example. 
     FIG. 9 shows a detailed diagram using the example illustrated in FIG. 8 for determining curve f of upsetting roller  6 . As shown in FIG. 1, curve f(i) should be comprised for each of the total of three passes i(=1, 2, 3), of two straight-line segments, which are described by a total of four parameters a 1 (i), a 2 (i), l 1 (i), l 2 (i). Process parameters x and X nach , which are relevant for determining curve f, include band width distribution b(i), band thickness d(i), and band temperature T(i) after each pass i, width reduction Δb(i) and thickness reduction Δd(i) of band  4  after each pass i, as well as a coefficient α as a measure of the material hardness (deformation strength) of band  4 . 
     Curve parameters a 1 (i) and a 2 (i), i.e., the position correction values, are predicted for all three passes i by a neural network  142 , which has six network outputs o k (=0 . . . 5) for this purpose. Position correction values a 1 (i) and a 2 (i) are obtained as the product of network outputs o k  located between −1 and +1 and the respective width reductions Δb(i) of band  4 . As a result, none of position correction values a 1 (i) and a 2 (i) can be greater than the respective width reduction Δb(i). 
     Length coordinates l 1 (i) and l 2 (i) are determined by a device  19  as empirical values. Length coordinate l 2 (i), which corresponds to the length of the area of influence of upsetting rollers  6  in the first pass on band  4 , is established as 3 times the slab width for the band head and as twice the slab width for the band foot, for example. For the subsequent passes, the length of the area of influence of upsetting rollers  6  is halved each time, so that l 2 ( 2 )=½ l 2 ( 1 ) and l 2 ( 3 )=½ l 2 ( 1 ). The other length coordinates are established as l 1 (i)=⅓ l 2 (i). The values thus determined for the length coordinates refer to band  4  after it exits from mill train  3  when the band width distribution is measured. To drive upsetting rollers  6  in the individual passes i, these values must therefore be recalculated in each pass to the band length upstream from each pass i compared to the length of band  4  after exiting mill train  3  due to the band stretch caused by mill train  3 . This recalculation is performed on the basis of the temperature T(i), width b(i) and thickness d(i) of band  4  upstream from the respective pass i, the temperature, width and thickness of band  4  after exiting mill train  3  and the expansion coefficient α. 
     Curve parameters a 1 (i) and a 2 (i), predicted by neural network  142  on the basis of precalculated process parameters x, and curve parameters l 1 (i) and l 2 (i), predefined by unit  19 , are supplied to base automation unit  9  to adjust mill train  3 . In rolling band  4  in mill train  3 , band width distribution yactual and curve factual of the upsetting rollers  6  are measured by measured value detection device  10  and width measuring device  15  at discrete points. First, error Δy between the predefined specified band width distribution y set point  and the measured actual band width distribution yactual and then the specified curve f set point  is computed from measured curve factualand error Δy in unit  20  at, in this case, seven predefined points j(=0 . . . 6). Values f set point, j  of specified curve f set point  at these points are calculated as the sum of all passes i, i.e., specified curve fset pointis the sum of specified curves f set point (i) of the individual passes i. 
     On the basis of the recalculated process parameters x nach  supplied to it after the passage of band  4  through mill train  3 , neural network  142  delivers predictions on the position correction values a 1  (i) and a 2  (i), from which discrete values f j  of the predicted position correction values a 1  (i) and a 2  (i) of predicted total curve f are calculated as the sum for all passes i in a unit  21  at joints j. 
     Error Δf j =f set point,j −f j  is determined in a unit  22  by comparing discrete values f set point,j  of the sum specified curve fset pointwith the discrete values f j  of the predicted sum curve f. The squared error summed over all discrete points        E   =       1   2            ∑     j   =   o     6          Δ                   f   j   2                                  
     is formed from error Δf j  in an additional unit  23  and is used to adapt neural network  142  by the gradient method. 
     As mentioned previously, mill train  3  of the embodiment shown in FIG. 1 is a cogging train. In order to also take into account the effect of the subsequent process lines, such as the finishing train and the cooling section, this effect is measured at the end of the cooling section and supplied to device  13  for determining curve parameters s.