Accelerating Numerical Modeling and Optimization of Structural Mechanical Systems
Abstract
This research proposal presents Bayesian optimization and reduced order modeling methods to accelerate numerical analysis and design of structure mechanical system. First, a holistic framework of Bayesian optimization (BO) based on parameterized numerical models and genetic algorithm-guided adaptive sampling is developed to automate and accelerate the design of a front-loading washing machine. The research aims to address challenges associated with the model parameterization and global optimization and design. A multibody dynamics model of the washing machine incorporating a set of 9 key design variables is developed. The design variables are implemented to enable automated modifications of the dynamics model for certain parameters. This dynamics model is employed to perform a series of numerical simulations by considering a range of parametric values for the design variables. Numerical convergence analysis is performed to ensure that the simulation solutions remain accurate. Using the simulation solutions, the time histories of displacements at sensor locations of the washing machine during operation (from transient till steady-state motion) can be analyzed to understand how the natural frequencies of the washing machine are affected by various design variables. A sensitivity analysis is carried out to determine the design variables that have the strongest impact on the dynamic behavior of the washing machine. Subsequently, a BO-based design optimization approach is formulated for the fully parametrized front-loading washing machine model. Due to the complex relationship between the vibrational dynamics and design variables, a computationally efficient BO framework is be developed, in which a Gaussian process model and Genetic Algorithm (GA) are utilized along with carefully selected acquisition functions to enable adaptive sampling and search for optimal design values. The objective function is to minimize the maximum amplitude of the tub displacement inside the washing machine body. The fully parametrized front-loading washing machine model is investigated to verify that the model is applicable for parametric simulation and design optimization. In the next part of this proposal, a reduced order modeling (ROM) approach is presented to accelerate the static and buckling analysis of a thin-walled stiffened plate. Thin-walled stiffened plates are widely used for lightweight structural design but can be susceptible to buckling-induced instability failures. An accurate and efficient model is essential for optimizing stiffener size and shape and analyzing buckling while considering geometric complexity, location, loading, and boundary conditions. Recently, a non-conformal mesh method based on an inverse isoperimetric mapping algorithm (IIMA) was developed to efficiently model stiffened plates with complex-shaped stiffeners while keeping the base plate unchanged. Built on this work, a reduced order modeling (ROM) approach is introduced to reduce the computational cost of the response calculation of the static and buckling analysis of the stiffened plate. The principle is to use the base plate's free-vibration modal shapes as the projection subspace to estimate the displacement of the base plate and link its ROM prediction with stiffeners through displacement compatibility constraints at the interface. ROM is used again to approximate the eigenvalues in the buckling analysis of the stiffened plate. The proposed approach is investigated to examine if the approximated displacement and eigenvalues have significant effect in reducing the computational orders and complexities. Later the two separate ROMs for efficient static and buckling analysis is integrated with the topology optimization of a thin-walled stiffened plate modeled using a non-conformal mesh based finite element model. The optimization process has multiple iterations, with simulation responses at each iteration being computed either through a high-fidelity Full Order Model (FOM) or a ROM. The optimization procedure is automated utilizing two online decision-making modules that alternate the structural analysis between FOM and ROM to improve computational efficiency while preserving the requisite accuracy levels. A Proper Orthogonal Decomposition (POD)-ROM approach is formulated to obtain initial projection subspace and update projection subspace on-the-fly for both static and dynamic solutions. The results demonstrate salient efficiency and accuracy when incorporating ROMs into the optimization algorithm, with the optimized stiffener configuration closely matching the model generated using the original FOM. In future work, this research will address additional computational challenges in structural design optimization, specifically reducing complexity and costs associated with the 1) Jacobian computation and 2) online Proper Orthogonal Decomposition (POD). Methods to tackle these computational challenges will be investigated and examined to evaluate their efficiency individually. For the first method, previously introduced ROMs will be integrated with Jacobian computation. For the second challenge, the incremental Singular Value Decomposition (iSVD) method will be investigated to solve POD and avoid redundant calculations.