Using High-fidelity Time-Domain Simulation Data to Construct Multi-fidelity State Derivative Function Surrogate Models for use in Control and Optimization

Models that balance accuracy against computational costs are advantageous when designing dynamic systems with optimization studies, as several hundred predictive function evaluations might be necessary to identify the optimal solution. The efficacy and use of derivative function surrogate models (DFSMs), or approximate models of the state derivative function, have been well-established in the literature. However, previous studies have assumed an a priori state dynamic model is available that can be directly evaluated to construct the DFSM. In this article, we propose an approach to extract the state derivative information from system simulations using piecewise polynomial approximations. Once the required information is available, we propose a multi-fidelity DFSM approach as a predictive model for the system's dynamic response. This multi-fidelity model consists of summation between a linear-fit lower-fidelity model and an additional nonlinear error corrective function that compensates for the error between the high-fidelity simulations and low-fidelity models. We validate the model by comparing the simulation results from the DFSM to the high-fidelity tools. The DFSM model is, on average, five times faster than the high-fidelity tools while capturing the key time domain and power spectral density~(PSD) trends. Then, an optimal control study using the DFSM is conducted with outcomes showing that the DFSM approach can be used for complex systems like floating offshore wind turbines~(FOWTs) and help identify control trends and trade-offs.Comment: 14 pages,45 figure

Some efficient open-loop control solution strategies for dynamic optimization problems and control co-design

2021 Summer.Includes bibliographical references.This thesis explores strategies to efficiently solve dynamic optimization (DO) and control codesign (CCD) problems that arise in early-stage system design studies. The task of design optimization of dynamic systems involves identifying optimal values of the physical elements of the system and the inputs to effectively control the dynamic behavior of the system to achieve peak performance. The problem becomes more complex when designing multidisciplinary systems, where the coupling between disciplines must be accounted for to achieve optimal performance. Developing tools and strategies to efficiently and accurately solve these problems is needed. Conventional design practices involve sequentially optimizing the plant parameters and then identifying a control scheme for the given plant design. This sequential design procedure does not often produce system-level optimal solutions. Control co-design or CCD is a design paradigm that seeks to find system-level optimal design through simultaneous optimization of the plant and control variables. In this work, both the plant and controls optimization are framed as a integrated DO problem. We focus on a class of direct methods called direct transcription (DT) to solve these DO problems. We start with a subclass of nonlinear dynamic optimization (NLDO) problems for the first study, namely linear-quadratic dynamic optimization problems (LQDO). For this class of problems, the objective function is quadratic, and the constraints are linear. Highly efficient and accurate computational tools have been developed for solving LQDO problems on account of their linear and quadratic problem elements. Their structure facilities the development of automated solvers. We identify the factors that enable creating these efficient tools and leverage them towards solving NLDO problems. We explore three different strategies to solve NLDO problems using LQDO elements, and analyze the requirements and limits of each approach. Though multiple studies have used one of the methods to solve a given CCD problem, there isa lack of investigations identifying the trade-offs between the nested and simultaneous CCD, two commonly used methods. We build on the results from the first study and solve a detailed active suspension design using both the nested and simultaneous CCD methods. We look at the impact of derivative methods, tolerance, and the number of discretization points on the solution accuracy and computational times. We use the implementation and results from this study to form some heuristics to choose between simultaneous and nested CCD methods. A third study involves CCD of a floating offshore wind turbine using the levelized cost of energy (LCOE) as an objective. The methods and tools developed in the previous studies have been applied toward solving a complex engineering design problem. The results show that the impact of optimal control strategies and the importance of adopting an integrated approach for designing FOWTs to lower the LCOE