Model updating in structural dynamics: advanced parametrization, optimal regularization, and symmetry considerations

Numerical models are pervasive tools in science and engineering for simulation, design, and assessment of physical systems. In structural engineering, finite element (FE) models are extensively used to predict responses and estimate risk for built structures. While FE models attempt to exactly replicate the physics of their corresponding structures, discrepancies always exist between measured and model output responses. Discrepancies are related to aleatoric uncertainties, such as measurement noise, and epistemic uncertainties, such as modeling errors. Epistemic uncertainties indicate that the FE model may not fully represent the built structure, greatly limiting its utility for simulation and structural assessment. Model updating is used to reduce error between measurement and model-output responses through adjustment of uncertain FE model parameters, typically using data from structural vibration studies. However, the model updating problem is often ill-posed with more unknown parameters than available data, such that parameters cannot be uniquely inferred from the data. This dissertation focuses on two approaches to remedy ill-posedness in FE model updating: parametrization and regularization. Parametrization produces a reduced set of updating parameters to estimate, thereby improving posedness. An ideal parametrization should incorporate model uncertainties, effectively reduce errors, and use as few parameters as possible. This is a challenging task since a large number of candidate parametrizations are available in any model updating problem. To ameliorate this, three new parametrization techniques are proposed: improved parameter clustering with residual-based weighting, singular vector decomposition-based parametrization, and incremental reparametrization. All of these methods utilize local system sensitivity information, providing effective reduced-order parametrizations which incorporate FE model uncertainties. The other focus of this dissertation is regularization, which improves posedness by providing additional constraints on the updating problem, such as a minimum-norm parameter solution constraint. Optimal regularization is proposed for use in model updating to provide an optimal balance between residual reduction and parameter change minimization. This approach links computationally-efficient deterministic model updating with asymptotic Bayesian inference to provide regularization based on maximal model evidence. Estimates are also provided for uncertainties and model evidence, along with an interesting measure of parameter efficiency

Finite element model updating using objective-consistent sensitivity-based parameter clustering and Bayesian regularization

Finite element model updating seeks to modify a structural model to reduce discrepancies between predicted and measured data, often from vibration studies. An updated model provides more accurate prediction of structural behavior in future analyses. Sensitivity-based parameter clustering and regularization are two techniques used to improve model updating solutions, particularly for high-dimensional parameter spaces and ill-posed updating problems. In this paper, a novel parameter clustering scheme is proposed which considers the structure of the objective function to facilitate simultaneous updating of disparate data, such as natural frequencies and mode shapes. In a small-scale updating example with simulated data, the proposed clustering scheme is shown to provide moderate to excellent improvement over existing parameter clustering methods, depending on the accuracy of initial model. A full-scale updating example on a large suspension bridge shows similar improvement using the proposed parametrization scheme. Levenberg-Marquardt minimization with Bayesian regularization is also implemented, providing an optimal regularized solution and insight into parametrization efficiency

Symmetry properties of natural frequency and mode shape sensitivities in symmetric structures

When updating a finite element (FE) model to match the measured properties of its corresponding structure, the sensitivities of FE model outputs to parameter changes are of significant interest. These sensitivities form the core of sensitivity-based model updating algorithms, but they are also used for developing reduced parametrizations, such as in subset selection and clustering. In this work, the sensitivities of natural frequencies and mode shapes are studied for structures having at least one plane of reflectional symmetry. It is first shown that the mode shapes of these structures are either symmetric and anti-symmetric, which is used to prove that natural frequency sensitivities are equal for symmetric parameters. Conversely, mode shape sensitivities are shown to be unequal for symmetric parameters, as measured by cosine distance. These topics are explored with a small numerical example, where it is noted that mode shape sensitivities for symmetric parameters exhibit similar properties to asymmetric parameters

Sensitivity‐based singular value decomposition parametrization and optimal regularization in finite element model updating

Model updating is used to reduce error between measured structural responses and corresponding finite element (FE) model outputs, which allows accurate prediction of structural behavior in future analyses. In this work, reduced‐order parametrizations of an underlying FE model are developed from singular value decomposition (SVD) of the sensitivity matrix, thereby improving efficiency and posedness in model updating. A deterministic error minimization scheme is combined with asymptotic Bayesian inference to provide optimal regularization with estimates for model evidence and parameter efficiency. Natural frequencies and mode shapes are targeted for updating in a small‐scale example with simulated data and a full‐scale example with real data. In both cases, SVD‐based parametrization is shown to have good or better results than subset selection with very strong results on the full‐scale model, as assessed by Bayes factor

Mangrove microniches determine the structural and functional diversity of enriched petroleum hydrocarbon-degrading consortia

In this study, the combination of culture enrichments and molecular tools was used to identify bacterial guilds, plasmids and functional genes potentially important in the process of petroleum hydrocarbon (PH) decontamination in mangrove microniches (rhizospheres and bulk sediment). In addition, we aimed to recover PH-degrading consortia (PHDC) for future use in remediation strategies. The PHDC were enriched with petroleum from rhizosphere and bulk sediment samples taken from a mangrove chronically polluted with oil hydrocarbons. Southern blot hybridization (SBH) assays of PCR amplicons from environmental DNA before enrichments resulted in weak positive signals for the functional gene types targeted, suggesting that PH-degrading genotypes and plasmids were in low abundance in the rhizosphere and bulk sediments. However, after enrichment, these genes were detected and strong microniche-dependent differences in the abundance and composition of hydrocarbonoclastic bacterial populations, plasmids (IncP-1 alpha, IncP-1 beta, IncP-7 and IncP-9) and functional genes (naphthalene, extradiol and intradiol dioxygenases) were revealed by in-depth molecular analyses [PCR-denaturing gradient gel electrophoresis and hybridization (SBH and microarray)]. Our results suggest that, despite the low abundance of PH-degrading genes and plasmids in the environmental samples, the original bacterial composition of the mangrove microniches determined the structural and functional diversity of the PHDC enriched.Deutsche Forschungsgemeinschaft [SM59/4-1, 4-2]; FAPERJ-Brazil; European Commission [003998, 211684]; Alexander-von-Humboldt-Stiftung; CONICET (Argentina)info:eu-repo/semantics/publishedVersio

Enhancer of RNA polymerase III gene transcription.

A protein responsible for enhanced transcription by RNA polymerase III was identified in extracts from Xenopus oocytes. This protein, called EP3, interacts with a specific DNA sequence adjacent to the 3'-end of a Xenopus somatic 5S RNA gene and forms a distinct band shift complex with a unique DNase I footprint. Enhanced transcription was observed from both 5S RNA and tRNA reporter genes when EP3 binding sites were inserted at different locations and orientations. Removal of the EP3 protein from an oocyte extract abolished this enhanced transcription. In addition, EP3 was shown to stimulate transcription by increasing the rate of transcription complex assembly. EP3 directly discriminates between the somatic and oocyte 5S RNA gene families and may play a significant role in their differential expression during early Xenopus development

Bead-shift isolation of protein--DNA complexes on a 5S RNA gene.

Specific protein-DNA complexes formed on a Xenopus 5S RNA gene were isolated and characterized using a novel technique. A DNA template reversibly immobilized on paramagnetic beads was used to capture, affinity purify, and concentrate protein--DNA complexes formed in a whole cell extract. The complexes were then released from the beads in a soluble and transcriptionally active form via restriction enzyme digestion of the DNA. A band-shift gel was used to separate and obtain the DNase I footprints of five individual complexes. Three of the complexes resulted from the independent binding of two proteins, TFIIIA and an unidentified protein binding to a large region just downstream of the 3' end of the gene. Two more slowly migrating complexes contained an additional large central protected region covering most of the gene. The most slowly migrating complex displayed protein interactions over the 5' flanking sequences. The formation of two of these complexes was shown to be dependent on TFIIIC activity. The correlation between transcriptional activity and the formation of these complexes suggests that the observed protein--DNA interactions are important for transcription of 5S RNA genes