A Goal-Oriented, Sequential, Inverse Design Method for the Horizontal Integration of a Multistage Hot Rod Rolling System

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Nellippallil, A. B., Song, K. N., Goh, C.-H., Zagade, P., Gautham, B., Allen, J. K., and Mistree, F., 2017, "A Goal-Oriented, Sequential, Inverse Design Method for the Horizontal Integration of a Multi-Stage Hot Rod Rolling System," Journal of Mechanical Design, vol. 139, no. 3, pp. 031403.


The steel manufacturing process is characterized by the requirement of expeditious development of high quality products at low cost through the effective use of available resources. Identifying solutions that meet the conflicting commercially imperative goals of such process chains is hard using traditional search techniques. The complexity in such a problem increases due to the presence of a large number of design variables, constraints and bounds, conflicting goals and the complex sequential relationships of the different stages of manufacturing. A classic example of such a manufacturing problem is the design of a rolling system for manufacturing a steel rod. This is a sequential process in which information flows from first rolling stage/pass to the last rolling pass and the decisions made at first pass influence the decisions that are made at the later passes. In this context, we define horizontal integration as the facilitation of information flow from one stage to another thereby establishing the integration of manufacturing stages to realize the end product. In this paper, we present an inverse design method based on well established empirical models and response surface models developed through simulation experiments (finite-element based) along with the compromise decision support problem (cDSP) construct to support integrated information flow across different stages of a multistage hot rod rolling system. The method is goal-oriented because the design decisions are first made based on the end requirements identified for the process at the last rolling pass and these decisions are then passed to the preceding rolling passes following the sequential order in an inverse manner to design the entire rolling process chain to achieve the horizontal integration of stages. We illustrate the efficacy of the method by carrying out the design of a multistage rolling system. We formulate the cDSP for the second and fourth pass of a four pass rolling chain. The stages are designed by sequentially passing the design information obtained after exercising the cDSP for the last pass for different scenarios and identifying the best combination of design variables that satisfies the conflicting goals. The cDSP for the second pass helps in integrated information flow from fourth to first pass and in meeting specified goals imposed by the fourth and third passes. The end goals identified for this problem for the fourth pass are minimization of ovality (quality) of rod, maximization of throughput (productivity), and minimization of rolling load (performance and cost). The method can be instantiated for other multistage manufacturing processes such as the steel making process chain having several unit operations. [DOI: 10.1115/1.4035555]

Authors: Anand Balu Nellippallil, Kevin N. Song, Chung-Hyun Goh, Pramod Zagade, BP Gautham, Janet K. Allen, Farrokh Mistree

Corresponding Author: [Janet K. Allen, John and Mary Moore Chair and Professor, School of Industrial and Systems Engineering, University of Oklahoma, E-mail: janet.allen@ou.edu]

The Compromise Decision Support Problem Construct

Figure 1: The cDSP formulation

In the model-based realization of complex systems, we have to deal with models that are typically incomplete, inaccurate, and not of equal fidelity. This brings into the design process the different types of uncertainties associated with the system, the parameters considered, the models considered, and the uncertainties due to their interactions. [1] From the decision-based design perspective, the fundamental role of a human designer is to make decisions given the uncertainties associated. In this regard, we define robust design as design that is relatively insensitive to changes. This involves achieving a desired performance for the system, while the sensitivity of the performance objectives with respect to the system variables are minimized. Thus, the designer’s objective here is to find satisficing solutions that showcase good performance given the presence of uncertainties and not optimum solutions that are valid for narrow range of conditions, while performing poorly when the conditions are changed slightly. The cDSP is proposed by Mistree and coauthors for robust design with multiple goals.[2] [3] The fundamental assumption here is that the models are not complete and accurate; opposed to the fundamental assumption in optimization where the models are complete and accurate, and the objective function can be modeled accurately so that the solution obtained is implementable. Hence, the cDSP construct is anchored in the robust design paradigm first proposed by Taguchi.[4] Using the cDSP construct, several solutions are identified by carrying out trade-offs among multiple conflicting goals. The obtained solutions are then evaluated by carrying out solution space exploration in order to identify the best solutions that satisfy the specific requirements identified. The cDSP is a hybrid formulation based on mathematical programming and goal programming. In goal programming, the target values for each goals are defined, and the emphasis is on achieving the target for each goal as close as possible. In cDSP, different weights are assigned to these goals and the compromised solutions obtained for different appropriate weights are explored. The generic formulation of cDSP is shown in Fig. 1.

Goal-Oriented, Inverse Decision-Based Design Method

Figure 2: Goal-oriented, inverse decision-based design method for manufacturing stages having sequential flow of information

This goal-oriented sequential inverse decision-based design method proposed to design the rolling system is explained using the information flow diagram shown in Fig. 2 in the citation provided above. Please refer to the same for details.


  1. McDowell, D. L., Panchal, J., Choi, H.-J., Seepersad, C., Allen, J. K., and Mistree, F., 2010, Integrated Design of Multiscale, Multifunctional Materials and Products, Elsevier, New York.
  2. Mistree, F., Hughes, O. F., and Bras, B., 1993, “Compromise Decision Support Problem and the Adaptive Linear Programming Algorithm,” Structural Optimization: Status and Promise, M. P. Kamat, ed., AIAA, Washington DC., pp. 247–286.
  3. Bras, B., and Mistree, F., 1993, “Robust Design Using Compromise Decision Support Problems,” Eng. Optim., 21(3), pp. 213–239.
  4. Taguchi, G., 1986, “Introduction to Quality Engineering,” Asian Productivity Organization, Distributed by the American Supplier Institute, Dearborn, MI.
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