Efficient stochastic optimization algorithms for performance-based system design with application to structural control system design for floating offshore wind turbines

• Main Author: Gong, Fanming
• Other Authors: Cheung Sai Hung
• Format: Theses and Dissertations
• Language: English
• Published: 2019
• Subjects: Engineering::Civil engineering::Structures and design
• Online Access: https://hdl.handle.net/10356/103732; http://hdl.handle.net/10220/49986
• Institution: Nanyang Technological University

Performance-based system design optimization is always required in modern engineering applications. However, the available information about the system is never complete due to the uncertainties in the model parameters of the system, the future environmental conditions subjected to the system and the measurements or prediction errors in the system performance. This leads to a robust stochastic design optimization where all uncertainties of interest can be taken into account and the design objective function is regarded as the expectation of the performance function in the corresponding uncertain space. In practice, the objective function of such optimization problem can rarely be evaluated analytically, and its estimation may require much computational cost and involve unavoidable estimation errors. These features make robust performance-based system design challenging. This thesis aims to propose efficient algorithms to solve these stochastic optimization problems. The proposed algorithms are based on the basic idea by regarding the design variables as artificial random variables such that the sensitivity of the objective function can be explored by investigating the marginal probability density function (PDF) of the auxiliary PDF which is related to the performance function. This thesis proposes a new sampling algorithm ARS-SS (Acceptance-rejection Sampling with Subset Simulation) to reduce the computational cost required by simulating samples from the auxiliary PDF. Moreover, the BSP (Bayesian Sequential Partitioning) method, which is suitable for estimating high-dimensional PDFs, is adopted to estimate the marginal PDF based on the simulated samples and a new stochastic optimization algorithm (BSP with ARS-SS) is proposed by integrating the new sampling algorithm with BSP to solve stochastic optimization problems. This work also proposes an efficient algorithm to simultaneously solve multiple optimization problems for a single system with the computational cost which is comparable to the cost required by a single optimization problem. The effect of the statistical models for the environmental conditions on the performance of the system and the optimal design are studied in this work. The proposed algorithms are used to identify the optimal design of structural control system for floating wind turbines. The random variables of interest include four main random variables which characterize the sea states and millions of white Gaussian noise random variables to model the wind turbulences and stochastic waves. The dynamic response of the coupled controller and floating wind turbine system is obtained by a high-fidelity nonlinear simulator FAST-SC (Fatigue, Aerodynamics, Structures and Turbulence, Structural Control). This design optimization is also used as the case study to demonstrate the efficiency of the proposed algorithms. The optimal structural control system identified by the proposed algorithm can reduce the fatigue damage at the tower base by as much as 33% compared with the case without a control system. The case studies show the efficiency enhancement of ARS-SS, the ability and advantages of the proposed stochastic optimization algorithm in solving performance-based system design problems, the ability in saving computational cost of the proposed algorithm in solving multiple optimization problems for a single system and the effect of the statistical models on the optimal design.