AN RBF BASED HIGH-DIMENSIONAL MODEL REDUCTION APPROACH IN BUILDING OPTIMIZATION

Building optimization has gained importance with the recent push to create the most economical and efficient buildings possible. As the effects of optimization are a function of the building size, it is crucial to understand and further develop optimization techniques for large-scale building structures. Practical structural optimization of buildings requires the use of a structural analysis software package and an iterative optimization procedure. As a result, finite element (FE) software shall be linked with an optimization solver. It is an expensive process which requires extensive computer coding. Alternative methods are available, including metamodeling methods, which are used to create simple and approximate functions based on complex FE simulations. In this study, the approximate functions are generated using a high-dimensional model representation (HDMR) framework. The HDMR framework is a model reduction approach and is found to be very accurate for different functions. The component functions of HDMR are expressed using augmented radial basis functions (RBFs). To further improve the numerical efficiency of the metamodels and reduce the total required number of structural analyses, a few different HDMR sampling approaches are investigated, including one static approach and two iterative strategies. An existing nonlinear programming (NLP) solver is employed in the design process. To illustrate the proposed approach, a three-dimensional building structure is selected as a numerical example. The numerical optimization is conducted to reduce the torsional response of the building. The proposed optimization method works very well and the results from different HDMR techniques are compared.

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BUILDING STRUCTURE OPTIMIZATION BASED ON A HIGH-DIMENSIONAL MODEL REPRESENTATION APPROACH

Proceedings of International Structural Engineering and Construction ◽

10.14455/isec.2020.7(2).str-11 ◽

2020 ◽

Vol 7 (2) ◽

Author(s):

Qian Wang ◽

Joseph Nafash

Keyword(s):

Design Optimization ◽

Model Reduction ◽

Model Representation ◽

High Dimensional ◽

High Dimensional Model Representation ◽

Optimization Approach ◽

Building Structures ◽

Dimensional Model ◽

Gradient Based ◽

Structural Responses

In this study, a model reduction technique based on a high-dimensional model representation (HDMR) approach was investigated and applied to design optimization of building structures. Those structures have long been designed using engineering intuition and an iterative trial-and-error method. In order to evaluate structural responses, a finite element (FE) analysis code is generally required. Gradient-based numerical algorithms and evolutionary algorithms are widely available and can be adopted to the design optimization of structures. An alternative category of optimization methods relies on approximate objective or constraint functions that can be created using various interpolation or regression techniques. In this work, the model reduction was achieved using augmented radial basis functions (RBFs) as component functions of HDMR. After sample points were generated along each variable axis, detailed FE analyses were conducted to evaluate building responses, which were used for constructing RBF-HDMR models of structural responses. The optimization was performed using a standard gradient-based numerical method. The accuracy of the RBF-HDMR could be improved if the optimal design point was added as an additional sample point. One advantage of the proposed optimization approach was that the interface programming with any existing FE code was not necessary. To illustrative the application of the method, a high-rise building was studied and optimized in order to reduce the building’s global torsional responses. The proposed optimization method worked well for the example.

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