pproach, the pulsed laser is directed to impinge on the molten pool, setting up stress waves that are transmitted through the workpiece and picked up by the EMAT receiver. Modeling Weld process models intended for control purposes are characterized by the need to be computable in real time. This rules out many of the more exact numerical models that have been developed for finite element and nite difference methods. However, these computationally intensive numerical models may be quite useful in developing simpler models that can be used in the control of multivariable weld feedback control systems. Another important aspect of process models used for control purposes is that they generally need to provide both static and d ic information Analytical Models Since the 1940s considerable research has been focused on developing steady-state models that would predict DWP, given a set of IWP. Easily computed analytical models, based solely on conductive heat transfer, are reasonably accurate but primarily are of value in establishing approximate relationships. Improvements to these arly analytical models have been proposed that permit obtaining a better match to actual conditions and that may be calibrated in real time; however, accuracy remains limited in the absence of modeling extensions that require computationally intensive numerical solution. Empirical and Statistical Models Other approaches taken to developing steady-state weld process models include: empirically derived relation- te, ps between the IWP and DWP, with coefficients chosen to match experimental data and statistically derived ationships. Both of these approaches have proven to possess only a limited range of applicability, and they do not lend themselves to real-time "tuning"in a multi-variable control system application. Artificial Neural Network Models A promising method based on an artificial neural network(ANN) has been studied and found to be accurate and computationally fast in the application mode. Furthermore, the ann can be refined at any time with the addition of new training data and thus promises a method of continuously adapting to the actual welding Andersen [1992] has reported the application of an ann to mapping between the IWP's arc current, travel speed, arc length, and plate thickness and the DwP's bead width and penetration for GTAW. A back-propa gation network, using 10 nodes in a single hidden layer Fig. 104.2), was used for the modeling. A variety of Speed different network configurations were initially evaluated for this purpose. Generally, it was found that one hidden layer was sufficient for weld modeling, and the best Lengt training rate was obtained with on the order of 5 to 20 nodes in the hidden layer. The same plate material was Plate Bead ssumed throughout the experiment, which eliminated Thickness the need for specifying any of the material parameters included thermal conductivity, diffusivity, etc. IGURE 104.2 A neural netw A total of 72 welds, produced on two material thick nesses of 3.175 and 6.350 mm, were used for the purpose of training and testing the network for modeling purposes. Weld current values of 80, 100, 120, and 140 A, travel speeds of 2.12, 2.75, and 3. 39 mm/s, and arc engths of 1.52, 2.03, and 2.54 mm were used. Eight of the welds, which were randomly selected, were not used in the training phase but were reserved for testing the model. with a learning rate parameter of 0.6 and a momentum term of 0.9, the network was trained for 200,000 iterations e 2000 by CRC Press LLC© 2000 by CRC Press LLC approach, the pulsed laser is directed to impinge on the molten pool, setting up stress waves that are transmitted through the workpiece and picked up by the EMAT receiver. Modeling Weld process models intended for control purposes are characterized by the need to be computable in real time. This rules out many of the more exact numerical models that have been developed for finite element and finite difference methods. However, these computationally intensive numerical models may be quite useful in developing simpler models that can be used in the control of multivariable weld feedback control systems. Another important aspect of process models used for control purposes is that they generally need to provide both static and dynamic information. Analytical Models Since the 1940s considerable research has been focused on developing steady-state models that would predict DWP, given a set of IWP. Easily computed analytical models, based solely on conductive heat transfer, are reasonably accurate but primarily are of value in establishing approximate relationships. Improvements to these early analytical models have been proposed that permit obtaining a better match to actual conditions and that may be calibrated in real time; however, accuracy remains limited in the absence of modeling extensions that require computationally intensive numerical solution. Empirical and Statistical Models Other approaches taken to developing steady-state weld process models include: empirically derived relation￾ships between the IWP and DWP, with coefficients chosen to match experimental data and statistically derived relationships. Both of these approaches have proven to possess only a limited range of applicability, and they do not lend themselves to real-time “tuning” in a multi-variable control system application. Artificial Neural Network Models A promising method based on an artificial neural network (ANN) has been studied and found to be accurate and computationally fast in the application mode. Furthermore, the ANN can be refined at any time with the addition of new training data and thus promises a method of continuously adapting to the actual welding conditions. Andersen [1992] has reported the application of an ANN to mapping between the IWP’s arc current, travel speed, arc length, and plate thickness and the DWP’s bead width and penetration for GTAW. A back-propa￾gation network, using 10 nodes in a single hidden layer (Fig. 104.2), was used for the modeling. A variety of different network configurations were initially evaluated for this purpose. Generally, it was found that one hidden layer was sufficient for weld modeling, and the best training rate was obtained with on the order of 5 to 20 nodes in the hidden layer. The same plate material was assumed throughout the experiment, which eliminated the need for specifying any of the material parameters. Otherwise, additional input parameters might have included thermal conductivity, diffusivity, etc. A total of 72 welds, produced on two material thick￾nesses of 3.175 and 6.350 mm, were used for the purpose of training and testing the network for modeling purposes. Weld current values of 80, 100, 120, and 140 A, travel speeds of 2.12, 2.75, and 3.39 mm/s, and arc lengths of 1.52, 2.03, and 2.54 mm were used. Eight of the welds, which were randomly selected, were not used in the training phase but were reserved for testing the model. With a learning rate parameter of 0.6 and a momentum term of 0.9, the network was trained for 200,000 iterations. FIGURE 104.2 A neural network used for weld modeling