Robust optimization based on knowledge discovery from metal forming simulation
Introduction
Knowledge-based engineering (KBE) has been used widely, which integrates artificial intelligence with CAX system and connects engineering design without interruption [1]. Numerical simulation is applied to predict forming defects and optimize process parameters. Numerical simulation generates massive data, in which large amounts of useful knowledge is hidden. Current approaches require scientists to manually search for anomalies, underlying patterns, and events of interest in simulation by scientific visualization techniques [2]. Thus much of the output of computational simulations is simply stored on disks and far from being fully used. Knowledge discovery in database (KDD) is the automatic extraction of non-obvious, hidden knowledge from large volumes of data, which grew out of the commercial areas [3]. Its great success in those areas has triggered our interest on its application in developing KBE system.
The general term “robust design” in engineering usually refers to the Taguchi statistical method [4], which has been used in many research areas. Robinson et al. [5] gave a general review of recent work done in the area of robust design since 1992. Cho et al. [6] proposed a set of enhanced optimization strategies by integrating robust and tolerance design. Gantois et al. [7] described a quite innovative multidisciplinary optimization method based on robust design techniques.
The problem with these researchers is that few papers have addressed the knowledge discovery and robust optimization simultaneously. In this paper, a knowledge discovery and robust optimization method for parameter optimization of metal forming processing based on simulation is introduced. First, a data-mining algorithm is developed to deal with the data of numerical simulation. Then, a robust optimization design method is presented to obtain the robust optimization parameter for metal forming processing.
Section snippets
Framework of robust optimization based on knowledge discovery from simulation
According to the characteristics of the metal forming simulation data, a framework of robust optimization based on knowledge discovery from simulation is proposed as shown in Fig. 1. It is composed of four parts: (1) product design and development, (2) data collection, (3) knowledge discovery, and (4) knowledge-based robust optimization.
Knowledge discovery from simulation data
The equivalence relation in basic rough set theory (RST) is too strict for quantitative data such as FEA simulation data. In this paper, we introduce fuzzy indiscernibility relation to replace the equivalence relation in basic RST. Then, the information processing scope can be extended greatly, and the generated productive rules are nearer to natural language, which help understanding the mined knowledge more clearly.
For a decision table S = (U, A ∪ {d}), if the value set Va is composed of
Robust optimization based on knowledge discovery
After rule sets is obtained by knowledge discovery, robust optimization process is implemented. In the model for robust parameter optimization, knowledge discovery-based rule sets is expressed as interval boxes, which are adopted to describe the uncertainty of design parameters quantitatively to enhance the design robustness. The model for robust optimization based on knowledge discovery is formulated as.
Given p and the tolerance of x and p: :
Example
An example of parameter design of extrusion-forging process is illustrated verify the validity of the above method of robust optimization based on knowledge discovery from metal forming simulation. Extrusion-forging is a common metal forming process for the mass production of middle-size or small forging parts. When the upper die is moving down, the material of the billet in the die gap will be forced simultaneously into the upper die orifice and the lateral gap. The configuration of the billet
Conclusions
This paper presents a knowledge discovery method from simulation and a robust optimization method. According to the characterization of metal forming simulation, a knowledge discovery method, which integrates the fuzzy-set and the rough-set concepts, is proposed. Secondly, the knowledge discovery result is considered in the robust optimization model, which is a new model to support parameter design of metal forming process. The robust optimization model is solved by Genetic Algorithm. Finally,
Acknowledgements
This paper is supported by the National Natural Science Foundation of China (Nos. 60304015 and 50575142).
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