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Content  WELDING RESEARCH S267WELDING JOURNAL ABSTRACT. Artificial neural network models that predict the Charpyimpact toughness values as a function of compo sition, heat treatment, and shielded metal arc welding process parameters were cou pled with multipurpose optimization soft ware. This coupled model was used to op timize the carbon, nickel, and manganese concentrations in a weld to achieve a max imum toughness of 120 J at –60°C. The coupled model used linear and nonlinear techniques to explore the possible combi nations of carbon, manganese, and nickel concentrations for a given set of welding process parameters. An optimum weld metal composition was achieved only with nonlinear methods. The number of itera tions and the exploration of input para meter space varied depending upon the type of nonlinear technique. The pre dicted weld metal composition was in agreement with published results. Introduction The development of a new welding consumable for a weldment with good properties is often difficult due to complex interaction between alloying elements, welding process, process parameters, and the testing conditions. Among this wide range of variables, it is not possible to vary one variable without influencing the effect caused by the other. For example, Evans showed that, for a given shielded metal arc welding process and process parameters, increasing the titanium concentration from 7 to 30 parts per million (ppmw) led to a large increase in the toughness of Fe CMnbased welds (Ref. 1). Though the concentration of titanium was varied, it in fluenced the effect of oxygen in the weld. In a similar manner, increasing nickel con centration in highmanganese (~2 wt%) steel welds did not improve the toughness of the weld as would be expected other wise. This phenomenon was explained with an increase in hardenability effect, i.e., increased nickel and manganese con centration led to the formation of marten site (Ref. 2). The above example illus trated the need for extensive trial and error experimentation guided by metal lurgical principles. In the last three decades, extensive research has been done on welding consumable design and there exists a large set of experimental data re lating the process, composition, and prop erties (Refs. 3–6). However, these welding consumable designs are not guaranteed to be the optimum, since it is not practical to explore all combinations of compositional and process variations due to the cost and time limitations. To arrive at an optimum composition and process parameters, an alternative ap proach is to use computational models that have been well tested and validated with already existing experimental data. Computational models relate the input parameters (e.g., voltage, current, weld metal composition, etc.) to the output pa rameters (strength, toughness, mi crostructure, etc.). These models can be empirical, phenomenological, or inte grated models (may include empirical and phenomenological models). Empirical models are either based on analytical functions or artificial neural network models that have been fitted or trained, respectively, on already existing data. The empirical models in general have limited extendibility to the range of input data used in the development stage. The phe nomenological models are based on well established principles or equations that describe particular phenomena. Many pa rameters used in the development of these models are derived from experimental in formation. The integrated models can couple many such models to relate the complex interactions between different phenomena. By interrogation of these computational models over the wide range of compositional and process para meters, it is possible to arrive at optimum composition by repeated calculations. Optimization of welding using compu tational models must consider two main issues. First, the models cannot be applic able to overall input space due to its limi tation on applicability. This can be solved by limiting the scope of the input data used in the calculations. Second, even with lim ited scope of input variables, this ap proach may sometimes lead to insolvabil ity conditions, depending on the input parameters space that needs to be consid ered for optimization. For example, in a case where ninput parameters are varied over a range of mvalues independently, the number of combinations that need to be evaluated by this forward modeling would amount to mn. In a steel weld metal, if the concentrations of nickel, silicon, and manganese are allowed to vary between 0 and 10 wt% with increments of 0.1, then the number of combinations to find the optimum will be 106. The 106evaluations can be easily performed for a simple model that requires resources of only a small desktop computer. For example, if a model takes 0.01 s for one calculation, it will take only 2.78 h. If the model takes 8 h to run a particular case, it will take 913 years! This problem of insolvability can be removed by extending the recent advances in optimization methodologies. The cur rent paper pertains to the evaluation of optimization software toward weld design optimization. SUPPLEMENT TO THE WELDING JOURNAL,OCTOBER 2004 Sponsored by the American Welding Society and the Welding Research Council Optimization of Shielded Metal Arc Weld Metal Composition for Charpy Toughness Artificial neural network models can help formulate consumables BY M. MURUGANANTH, S. S. BABU, AND S. A. DAVID M. MURUGANANTH, formerly at the Met als and Ceramics Division, Oak Ridge Na tional Laboratory, Oak Ridge Tenn., is at the School of Material Engineering, Nanyang Technological University, Singapore. S. S. BABU and S. A. DAVID are with the Metals and Ceramics Division, Oak Ridge National Laboratory. KEYWORDS Consumable Design Neural Network Modeling Optimization Methodologies Nonlinear Programming Sequential Quadratic Programming Downhill Simplex Methods Genetic Algorithms babu qwkcorr 8/27/04 8:35 AM Page 267 
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