Reliability and sustainability integrated design optimization for engineering structures with active machine learning technique

Recent strategic plans from many governments share the same emphasis on sustainable development goals. The construction industry is recognized as one of the primary contributors to greenhouse gas emissions. Stimulated by such political and practical requirements, this research aims to develop a reliability and sustainability integrated design optimization (RSIDO) framework for engineering structures. Statistical modelling is conducted which provides probabilistic models for embodied carbon coefficients (ECCs). The proposed RSIDO framework contains three main stages. The first stage solves the classical reliability-based design optimization (RBDO) problem. The second stage conducts the reliability-based embodied carbon quantification to define the sustainable reliability constraint. Lastly, the new sustainable probabilistic design constraint is embedded in the design question. Furthermore, to overcome the computational difficulty, an active-learning extended-support vector regression (AL-X-SVR) technique is proposed to improve the computational efficiency of the proposed framework. The embedded regression algorithm is presented with consolidated theoretical backgrounds. Further, an active learning strategy is implemented to select the learning samples efficiently. The applicability and effectiveness of the proposed AL-X-SVR method are demonstrated using a highly nonlinear-constrained mathematical validation. Additionally, the RSIDO framework is demonstrated through three engineering applications. This research contributes a comprehensive framework that not only addresses reliability and sustainability but also enhances computational efficiency, thereby introducing an innovative approach to design optimization in building engineering.