A CAD/CAE integrated framework for structural design optimization using sequential approximation optimization
Introduction
Structural design optimization has been an important and challenging topic in the field of engineering design for obtaining more efficient and lighter structures [1]. The aim of the design optimization is to determine the optimal shape of a structure to maximize or minimize a given criterion, such as maximizing the stiffness or minimizing the weight subjected to the constraint conditions of the stress or displacement. Modern commercial CAD (Computer Aided Design) and CAE (computer Aided Engineering) tools have become a quintessential part of structural design processes, which always require a loop of model-evaluate-remodel. However, many of them are usually stand-alone systems that are not designed for collaborative use [2], [3]. Mostly, these tools are confined to a single simulation because a designer usually has to work with two or more independent software packages for modeling and analysis, and the gap between the CAD and CAE domains is hard to get through. Hence an efficient CAD/CAE integrating approach is requisite to facilitate the structural design optimization [4], [5].
In the CAD/CAE integrated framework for structural design, optimization techniques are important in that they affect the accuracy, reliability, usability, and computing cost [6]. Over the past decade a number of optimization algorithms from gradient-based algorithms to evolutionary algorithms (EAs) as well as approximate-based optimization algorithms [7] have been widely used in structural optimization problems. Every foregoing optimization approach has its own advantages and disadvantages.
Examples of gradient-based optimization applied to structural design problems can be found in the literatures [8], [9]. Gradient-based optimization algorithms need the gradient information which is usually difficult to compute [10] or even unavailable. Moreover, they are prone to being trapped in local optima. A number of EAs such as genetic algorithm [11], simulated annealing [12], particle swarm optimization algorithm [13], immune algorithm [14], and artificial bee colony algorithm [15] have been widely used to solve structural design optimization problems. However, these methods require a huge number of function evaluations and the computational cost is extremely high [16], [17], which makes it difficult to apply these optimization techniques to the structural design directly. In recent years, approximation techniques such as response surface method (RSM) [18], [19], neural network (NN) [20], [21], polynomial regression models [22], Kriging methods [23] and radial basis function (RBF) [24] method are explored and exploited intensively. These techniques in association with the EAs are able to improve the computational efficiency [25] in structural optimization problems, while the disadvantage is the error between the meta-model and the true model, which will reduce the reliability of approximation-based optimization methods.
Lower computational cost, generality, robustness, and accuracy are all required for structural optimization processes [26]. Thus, a sequential approximate optimization (SAO) approach [27], [28] has gained popularity recently. Firstly, a small-size design of experiment (DOE) is employed to construct the surrogate model through various approximate techniques, then the global optimum of the response surface can be found by global optimization techniques such as EAs. If the termination criterion specified by the designer is satisfied, the SAO algorithm will be terminated. Otherwise, a few new sampling points will be added to improve the accuracy of the response surface. Through the iterative process, a highly accurate global optimum can be found with a small number of function evaluations in comparison with pure EAs. The high computational efficiency makes the SAO algorithm a promising optimization technique for the computation-intensive structural design problems.
However, the study of the SAO algorithm is still relatively young. A reliable and practical SAO algorithm is still lacking in the engineering design area. In SAO, the approximation technique and the sampling strategy are the two key elements for a successful optimization. In Section 2 the general formulation of the SAO approach is first presented, then a new method to determine the width of basis function for the RBF network and an adaptive sampling strategy are proposed to enhance the SAO algorithm. Furthermore, in order to exploit the SAO algorithm thoroughly in mechanical engineering, a framework that permits the integration between commercial CAD and CAE tools in conjunction with the SAO algorithm is developed. This approach widens the applications of the SAO method in structural design optimization problems. Moreover, this approach also facilitates the complex structural optimization process and makes it more convenient for engineering designers. Section 3 focuses on the general structural design optimization framework based on the SAO approach in association with CAD/CAE integration. Section 4 presents different case studies, which are used to demonstrate the efficacy of the integrated framework. Finally, the paper closes with some concluding remarks.
Section snippets
General framework of the SAO approach
A general structural optimization problem with constraints is considered as follows:
Here XL and XU is the upper and lower bound of design variables, respectively. For structural design problems, the objective function and constraints are usually implicit functions of design variables, usually obtained by finite element analysis (FEA).
In the classical approximation-based optimization process summarized in [28], accuracy of the surrogate
CAD/CAE integration for structural design optimization
SAO is proved to be a powerful optimization technique in solving structural optimization problems [40]. In mechanical practices, the structural analysis is usually based on the FEA in the high fidelity level (HFL), which is performed by professional CAE systems associated with specific CAD systems product design. However, CAD and CAE systems usually use different data formats to represent the design geometry [41], [42]. Though the design and analysis models in essence describe the same object,
Benchmark tests
In this section, two case studies from simple to complex, from low dimension to moderate-dimension are taken from the engineering practices to investigate the efficacy of the proposed framework. The effectiveness and robustness of the proposed SAO algorithm is validated in comparison with other optimization techniques in this section as well.
Conclusion
Modern engineering design processes often rely on complex computer-aided simulations to evaluate candidate designs. This research presents a structural design optimization framework based on the improved SAO algorithm in conjunction with the CAD/CAE integration. The approximation technique and the sampling strategy are the two key factors for a successful SAO algorithm. In this paper, a new method based on the local density of sampling points and the technique of cross validation is proposed to
Acknowledgements
The authors acknowledge Prof. Derek Ingham in College of Environmental and Materials Engineering of Leeds Uni. for his advices and comments throughout this work.
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