AN ADAPTIVE RBF METHOD FOR DESIGN OPTIMIZATION OF BUILDING STRUCTURES

Design of building structures has long been based on a trial-and-error iterative approach. Structural optimization provides practicing engineers an effective and efficient approach to replace the traditional design method. A numerical optimization algorithm, such as a gradient-based method or genetic algorithm (GA), can be applied, in conjunction with a finite element (FE) analysis program. The FE program is used to compute the structural responses, such as forces and displacements, which represent the design constraint functions. In this method, reading and writing the input/output files of the FE program and interface programming are required. Another method to perform structural optimization is to create an approximate constraint function, which involves implicit structural responses. This is referred to as a surrogate or metamodeling method. The structural responses can be expressed as approximate functions, based on a number of preselected sample points. In this study, an adaptive metamodeling method was studied and applied to a building structure. The FE analyses were first performed at the sample points, and metamodels were constructed. A gradient-based optimization algorithm was applied. Additional samples were generated and additional FE analyses were conducted so that the model accuracy could be improved, close to the optimal design points. This adaptive scheme was continued, until the objective function values converged. The method worked well and optimal designs were found within a few iterations.

A sequential sampling method for adaptive metamodeling using data with highly nonlinear relation between input and output parameters

Purpose Metamodeling is an effective method to approximate the relations between input and output parameters when significant efforts of experiments and simulations are required to collect the data to build the relations. This paper aims to develop a new sequential sampling method for adaptive metamodeling by using the data with highly nonlinear relation between input and output parameters. Design/methodology/approach In this method, the Latin hypercube sampling method is used to sample the initial data, and kriging method is used to construct the metamodel. In this work, input parameter values for collecting the next output data to update the currently achieved metamodel are determined based on qualities of data in both the input and output parameter spaces. Uniformity is used to evaluate data in the input parameter space. Leave-one-out errors and sensitivities are considered to evaluate data in the output parameter space. Findings This new method has been compared with the existing methods to demonstrate its effectiveness in approximation. This new method has also been compared with the existing methods in solving global optimization problems. An engineering case is used at last to verify the method further. Originality/value This paper provides an effective sequential sampling method for adaptive metamodeling to approximate highly nonlinear relations between input and output parameters.

AN ENGINEERING RELIABILITY ANALYSIS METHOD BASED ON ADAPTIVE METAMODELS

In practical engineering problems, numerical analyses using the finite element (FE) method or other methods are generally required to evaluate system responses including stresses and deformations. For problems involving expensive FE analyses, it is not efficient or straightforward to directly apply conventional sampling-based or gradient-based reliability analysis approaches. To reduce computational efforts, it is useful to develop efficient and accurate metamodeling techniques to replace the original FE analyses. In this work, an adaptive metamodeling technique and a First-Order Reliability Method (FORM) were integrated. In each adaptive iteration, a compactly supported radial basis function (RBF) was adopted and a metamodel was created to explicitly express a performance function. An alternate FORM was implemented to calculate reliability index of the current iteration. Based on the design point, additional samples were generated and added to the existing sample points to re-generate the metamodel. The accuracy of the RBF metamodel could be improved in the neighborhood of the design point at each iteration. This procedure continued until the convergence of the reliability analysis results was achieved. A numerical example was studied. The proposed adaptive approach worked well and reliability analysis results were found with a reasonable number of iterations.

Selecting process parameter in injection molding via simulation optimization

A simulation optimization method based on design of experiments and adaptive metamodeling techniques is applied in this work to set process parameters in injection molding. The proposed method is used first to select the best processing conditions to injection molding a disposable camera front plate in the presence of either a single performance measure or a composite function of a series of performance measures. Secondly, it is used to select the best injection gate configuration from three different injection scenarios, as well as the values of mold temperature and melt temperature for a real automotive part in order to minimize process variability. The optimization results are discussed in light of the performance of the simulation optimization method.