CE Ph.D. Dissertation
Wed, Dec 15, 2021
12:00 PM - 2:00 PM
Location: Zoom Meeting
Speaker: Xiaoshu Zeng, CE Ph.D. Candidate, Viterbi School- Astani Department of Civil and Environmental Engineering
Talk Title: Efficient Inverse Analysis with Dynamic and Stochastic Reductions for Large-Scale Models of Multi-Component Systems
Abstract: This work has two main goals: the primary goal of dealing with inverse analysis for large-scale models of multi-component systems and the second goal of dealing with the multi-fidelity uncertainty
quantification (UQ) for models with dissimilar parameterization. The primary goal involves efficient structural dynamic analysis, probabilistic modeling, and inverse analysis for the following reasons:
1. The context is the integrity assessment of the internals of a complex multi-scale structure, a fullyloaded spent nuclear fuel canister (FLSNFC), with the assessment based on dynamic signals on the
exterior surface of the FLSNFC before and after transportation.
2. Since the observed data is inevitably subjected to errors, the inverse analysis usually requires an accurate probabilistic model to capture the uncertainty propagated to the quantities of interest (QoI).
3. An efficient forward model, a dynamic model, is essential to construct a probabilistic model for complex systems.
A first attempt to build an efficient dynamic model is through constructing a global reduced-order basis (ROB). Usually, the complex multi-scale structures are characterized by numerous local vibration modes (or elastic modes) and the usual long-wavelength global vibration modes. Accordingly, a methodology that does not require the computation of the numerous local modes builds a global reduced-order model (ROM) by constructing a global ROB. In this method, the kinematics of the structure is modified to filter the local vibrations. Moreover, the reduced kinematics is combined with the idea of static condensation to achieve higher accuracy.
Due to the high accuracy requirement, a second attempt for dynamic modeling is carried out. For the FLSNFC, a honeycomb basket is placed inside the cylindrical canister, and a fuel assembly (FA)
that holds nearly 100 fuel rods is inserted in each of the 68 basket cells. A multi-level nested CraigBampton (CB) sub-structuring method with shift-invert Lanczos (SIL) eigenvalue solver and filtering of the local vibration modes of the substructures is proposed. This method is adapted to the multi-scale nature and localized connections between the substructures. The CB sub-structuring technique takes advantage of the limited degrees of freedom (DOF) of internal boundary and is applied to modal analysis for two structural levels, the system and the FA levels. As a result, the integrated method achieves a computational gain of four orders of magnitude for the FLSNFC at the expense of negligible errors.
For probabilistic modeling, polynomial chaos expansion (PCE) is an efficient method, but it suffers from the curse of dimensionality. However, a basis adaptation method proposed by Tipireddy and Ghanem (2014)  can reduce the dimension of the problem by rotating the input Gaussian random variables such that the quantity of interest (QoI) in the new space has concentrated representation. In this study, we proposed two novel approaches that can accelerate the convergence of the basis adaptation method. In the first approach, the mean and Gaussian coefficients in the adapted space are corrected by information obtained from a pilot PCE. The second approach updates the rotation matrix by taking advantage of the probabilistic information embedded in the higher dimensional adaptation gleaned from an initial adaptation. As a result, both approaches achieve accelerated convergence of the basis adaptation method with negligible additional costs.
The basis adaptation is adequate to reduce the dimension for the scalar QoI problems. To deal with UQ problems with high dimensional QoI and high dimensional parameter space, the integration of Karhunen- Loève expansion (KLE) and basis adaptation is proposed. The KLE first approximates the QoI to reduce the dimension of the QoI to a limited number of KL terms. Then, for each KL term, an adapted PCE is built with the accelerated basis adaptation method to reduce the dimension of the input variables. The PCE models of the KL terms then can be substituted back to the KLE of the QoI to obtain a surrogate probabilistic model of the QoI. Finally, the accuracy of the surrogate model is verified.
The Bayesian method will be used for the inverse analysis of parameter inference given observed data of a possibly damaged model. The process usually involves evaluating the forward model
numerous times, which is intractable for the complex system considered in the present study, even if the dynamic ROM is used. Thanks to the accurate surrogate probabilistic model of the QoI, the physical model required to be evaluated in Bayesian analysis can be replaced by the surrogate model to achieve several orders of computational efficiency. Nevertheless, generating posterior samples of high dimensional parameters can still be challenging. Thus, a block-update Markov Chain Monte Carlo (MCMC) method is applied to address this issue. By appropriately designing the inverse problem, the location and damage types of the internals can be identified based on dynamic signals on the exterior
The second goal of the work is to propose a novel multi-fidelity UQ method for dissimilar parameterization models. In multi-fidelity UQ, credible prediction and analyses of high-fidelity (HF) models are obtained by leveraging evaluations of a large number of efficient low-fidelity (LF) models.
The efficacy of the technique relies heavily on the correlation of the HF and LF models. We propose using the basis adaption method in the multi-fidelity technique to independently identify the important directions (or adapted variables) for each model, and the important directions assemble a common lower-dimensional space. Since important directions have concentrated information of the QoI and are aligned for different models, the samples generated on the common lower-dimensional manifold have
enhanced correlations. Thus, the proposed method can increase the performance of the multi-fidelity technique, especially for models with dissimilar parameterization.
The two main goals in the thesis are relevant since both involve stochastic reduction for complex multi- component models.
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