Finding the input specifications to obtain the specified performance of a component being designed is an essential activity of a designer. However, obtaining solutions for this inverse problem is a complex task; especially when there are multiple steps with many-to-one mappings at each step in the forward problem. This complexity is further augmented in the presence of uncertainty of the parameters and models used.

The typical heat treatment process involves multiple steps and the same outcome can possibly be achieved through multiple routes. Obtaining suitable process parameters for desired final properties such as the hardness profile is a requirement of the process design. In this work an error metric called the Hyper Dimensional Error Margin Index (HD_EMI) is used for inverse process chain design where the objective is to obtain the process set points in a sequence of heat treatment operations involving carburization, quenching and tempering processes. We have validated the solution of inverse problem by solving the detailed forward problem. The application procedure used in this study to solve inverse problem is simple and results obtained are encouraging for further exploration of HD_EMI.

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