Relevance vector machine and fuzzy system based multi-objective dynamic design optimization: A case study

doi:10.1016/j.eswa.2009.10.032

Expert Systems with Applications

Volume 37, Issue 5, May 2010, Pages 3598-3604

https://doi.org/10.1016/j.eswa.2009.10.032 Get rights and content

Abstract

To improve the original design flaws of overturning assembly of glass stacking machine taken as a case study, a multi-objective optimization approach integrated relevance vector machines (RVM), multi-objective genetic algorithms (MOGA) and fuzzy system are presented for the optimal dynamic design problem. Firstly, the multi-objectives of the overturning assembly are constructed by the use of dynamic structure optimization design theory. The motion simulation and finite element analysis of overturning assembly are utilized for sampling scheme given by uniform design to collect the train dataset. The dataset could describe the non-linear behaviors of dynamic and static characteristics of variety of mechanical structures, which is identified by RVMs. Sequentially, RVM- based meta-model as fitness function is combined with MOGA to obtain the Pareto optimal set. Finally, a fuzzy inference system is established as decision-making support to obtain the optimum preference solution. Therefore, the modified physical prototype with the round solution proofed feasibility and efficiency of this approach.

Introduction

In recent years, dynamic design methods, as an important aspect of modern design, are becoming increasingly common in the field of structural design problems, which can be effective in improving the dynamics performance and stability of equipment, reducing the costs of production. The objective function such as eigenvalue or structural response is a complex implicit non-linear function in the analysis of the dynamics. The huge computation burden is often caused by dynamic design analysis, simulation and optimization.

Wang and Shan (2007) described the meta-modeling technology in the optimization of engineering design. In the physical process analysis and simulation, in order to obtain a comparable level of accuracy as physical testing data and not too expensive computational consumption, the meta-modeling has been widely used in various disciplines, as well as in the field of engineering optimization. The meta-modeling is an approximation model used in the non-linear process modeling, no more than to approximate the non-linear finite element model. The statistical learning theory has been popularly developed in non-linear system regression based on input and output data with noise (Chan, Chan, & Cheung, 2001). Relevant vector machine (Tipping, 2001) (RVM) is the general Bayesian learning framework of kernel method for obtaining state-of-the art sparse solutions to regression and classification tasks, which lead to significant reduction in the expense of computational complexity of the decision function and memory consumption, thereby making it more suitable for meta-modeling applications. RVM in many applications (Yuan et al., 2007, Widodo et al., 2009) have produced very good results.

In dynamic design problem, a number of conflicting objectives should trade off. As a result, the dynamic design problem is in fact a highly non-linear, complex solution space-based multi-objective optimization problem, which has the complexity of a general multi-objective optimization but also has the inherent difficulty of dynamic design.

Glass stacking machine could have automatic unstacking glass sheets from stock stands and could have been transmitting the glass sheet to the glass-cutting table. There are some flaws in original glass stacking machine due to the application of traditional design methods: the 2 mm thickness of big glass sheets overturned by the stacking machine will be fragmentized, no sufficient accurate positioning, and unwieldy and unreasonable structure. As the glass overturning and transmission is a dynamic process, the dynamic properties are essential to the design. That is, it must be optimized with dynamic design methods to achieve smooth overturning process.

In this paper, in order to improve the product performance, a hybrid approach that integrated relevant vector machine, genetic algorithms and fuzzy inference system is presented to the multi-objective optimization problems of dynamic design. The key component of glass stacking machine - overturning assembly taken as a case study - instantiates the efficiency and feasibility of this approach.

Section snippets

Glass stacking machine

Glass stacking machine (shown in Fig. 1) is composed of frame, overturning assembly, conveying system, roller feeding system, hydraulic system and pneumatic system components. The overturning assembly mainly consists of overturning arm, overturning cylinder, lifting cylinder and sucker. According to the function decomposition, the overturning assembly should meet the following features:

1.
Could overturn the largest glass sheets of the original size of $6.0 m \times 3.3 m$ with thickness of $2 – 19 mm$ .
2.
Overturned

Multi-objective optimization of dynamic design of overturning assembly

Relevance vector machine (Tipping, 2001) is simply a specialization of a spares Bayesian model which utilizes the same data-dependent kernel basis. The key feature of RVM is that the inferred predictors are good in generalization performance, as well as exceedingly sparse in that they contain relatively few “relevance vectors”, which means shorter consuming prediction time. Therefore, a well-trained RVM is used as a fitness function in GA-based optimization for saving the fitness value

Discussion

The difference of test dataset between the prediction based on RVM and the finite element analysis is less than 3.56%, which meet the precision of engineering requirements. Furthermore, the computation time of prediction by RVM is hundred times faster than that of finite element analysis. To apply the ideal point approach, the dynamic multi-objective optimization functions could be changed to the quadratic programming model, thus the optimum results compared with this approach are shown in

Conclusion

In this paper, a hybrid intelligent approach that integrated RVM, GA and fuzzy inference system is proposed for the dynamic design of multi-objective optimization. To modify the original design flaw, the dynamic design- based three objectives and a performance constraint are given out for dynamic optimization design of overturning assembly as a case study. First, uniform design sampling strategy is adopted to acquire the samples dataset that reflects the dynamic characteristics of mechanical

Acknowledgements

This work is supported by the Science-Tech Tackle Key Project of Shandong Province of China (Grant No. 2007GG10009001) and also supported by National Science Foundation for Post-doctoral Scientists of China (Grant No.20090450700). The authors thank to Tao Wang for her help on the experimental work.

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Relevance vector machine and fuzzy system based multi-objective dynamic design optimization: A case study

Abstract

Introduction

Section snippets

Glass stacking machine

Multi-objective optimization of dynamic design of overturning assembly

Discussion

Conclusion

Acknowledgements

Engineering Application of Artificial Intelligence

Expert Systems with Applications

Engineering Applications of Artificial Intelligence

A fast and elitist multi-objective genetic algorithm: NSGA-II

IEEE Transactions on Evolutionary Computation

Number-theoretic methods in statistics