The research objective of this award is to develop innovative computational methods for solving random eigenvalue problems commonly encountered in modeling and simulation of high-dimensional stochastic dynamic systems. The proposed effort will involve: (1) a new polynomial dimensional decomposition (PDD) method for predicting the statistical moments and probability distributions of random eigensolutions; (2) a solid theoretical basis by quantifying approximation errors from the PDD and polynomial chaos expansion (PCE) methods; and (3) new multiplicative PDD, hybridization, and respective error analyses. The new PDD method will challenge or disrupt existing computational thinking, specifically by addressing highly nonlinear input-output transformations, large number of random variables, and arbitrarily large uncertainty of random input. Therefore, a long-standing stochastic problem associated with the curse of dimensionality will be alleviated to some degree, with positive ramifications in engineering and sciences. Deliverables include development of fast and reliable stochastic methods and algorithms, generation of modeling and simulation tools, documentation of research results, engineering student education, and hands-on experience for K-12 students.
If successful, the results of this research will be applicable to a broad range of industrial applications, such as civil, automotive, and aerospace infrastructure. Potential applications include analysis and design of civil structures; noise-vibration-harshness and crashworthiness of ground vehicle systems; and fatigue durability of aerospace structures. Beyond engineering, potential applications include nuclear physics, number theory, computational biology, among others, where random eigenvalue analysis plays a vital role. The transfer of knowledge created by this award will take place through organization of dynamics-related symposia, peer-reviewed journal publications, presentations at major conferences, software development, and student education. Educational goals include graduate student recruitment from an underrepresented minority group, implementation of software tools to upgrade existing courses at The University of Iowa, and active participation in Iowa?s Project Lead the Way program for middle- and high-school students.