Consider The Cognitive Uncertainty Of Multidisciplinary Design Optimization

There is coupling relationship between the disciplines of the multidisciplinary system. The traditional design approaches use the progressive design method, which fails to fully consider the coupling effect. For any expensive and complex multidisciplinary system, high quality and stable performance are the key objectives of its design, which may not be easily achieved by traditional design approaches. In recent years, the Multidisciplinary Design Optimization (MDO) appraoch has been proposed to handle the large-scale and complex system design in light of the concepts of Parallel Collaborative Design and Integrated Manufacturing Technology. The advantage of MDO is that it takes into consideration the highly coupling relationship of complex systems and thus can obtain the global optimal solution.In the product design process, there often exist a lot of uncertainties, which are classified into two categories in the literature, i.e., aleatory uncertainty and epistemic uncertainty. From the mathematical point of view, the background of the aleatory uncertainty is that there are adequate statistical data and the probability distributions can be known. The background of epistemic uncertainty is that there lack sufficient data/information to derive the probability distributions. In recent years, the design optimization under uncertainty has attacted more and more attention. In engineering practice, both aleatory uncertainty and epistemic uncertainty often exist. However, existing methods of MDO under uncertainty generally consider only the aleatory uncertainty, methods considering the epistemic uncertainty are quite rare. Therefore, this paper carries out the following researches:(1) Based on the probability theory and possibility theory, a single-disciplinary design optimization model is proposed which considers both aleatory and epistemic uncertainties. To solve the proposed model, a sequential optimization and concurrent uncertain assessment (SOCUA) optimization algorithm is proposed, which is based on the sequential optimization and reliability assessment (SORA) method which is effective in simplifying optimization algorithm structure and improving the computational efficiency. A numerical example and a real-life example are given to verify the feasibility and efficiency of the proposed model and algorithm.(2) Based on the performance measure analysis (PMA),which is a method that is effective in reducing the computational complexity of uncertain analysis, and three typical single-disciplinary optimization methods in MDO, three algorithms for possibility analysis in possibility-based multidisciplinary design optimization (PBMDO)are proposed, i.e., performance measure analysis-multidisciplinary feasible method (PMA-MDF), performance measure analysis-simultaneous analysis and design (PMA-SAND) and performance measure analysis-individual discipline feasible method (PMA-IDF). An example is given to verify the feasibility and to compare the efficiency of the three proposed algorithms.(3) Because multidisciplinary system often has epistemic uncertaint, possibility theory is introduced into MDO and the mathematical model of PBMDO is established. Three algorithms are proposed based on the framework of sequential optimization and possibility assessment (SOPA), i.e., possibility based multidisciplinary design optimization- sequential optimization and possibility assessment- multidisciplinary feasible method (PBMDO-SOPA-MDF), possibility based multidisciplinary design optimization- sequential optimization and possibility assessment- simultaneous analysis and design (PBMDO-SOPA-SAND) and possibility based multidisciplinary design optimization- sequential optimization and possibility assessment- individual discipline feasible method (PBMDO-SOPA-IDF). An example is given to verify the feasibility and to compare the efficiency of the three proposed algorithms.