Nonstationary response of structures and its application to earthquake engineering

This thesis presents a simplified state-variable method to solve for the nonstationary response of linear MDOF systems subjected to a modulated stationary excitation in both time and frequency domains. The resulting covariance matrix and evolutionary spectral density matrix of the response may be expressed as a product of a constant system matrix and a time-dependent matrix, the latter can be explicitly evaluated for most envelopes currently prevailing in engineering. The stationary correlation matrix of the response may be found by taking the limit of the covariance response when a unit step envelope is used. The reliability analysis can then be performed based on the first two moments of the response obtained.

The method presented facilitates obtaining explicit solutions for general linear MDOF systems and is flexible enough to be applied to different stochastic models of excitation such as the stationary models, modulated stationary models, filtered stationary models, and filtered modulated stationary models and their stochastic equivalents including the random pulse train model, filtered shot noise, and some ARMA models in earthquake engineering. This approach may also be readily incorporated into finite element codes for random vibration analysis of linear structures.

A set of explicit solutions for the response of simple linear structures subjected to modulated white noise earthquake models with four different envelopes are presented as illustration. In addition, the method has been applied to three selected topics of interest in earthquake engineering, namely, nonstationary analysis of primary-secondary systems with classical or nonclassical dampings, soil layer response and related structural reliability analysis, and the effect of the vertical components on seismic performance of structures. For all the three cases, explicit solutions are obtained, dynamic characteristics of structures are investigated, and some suggestions are given for aseismic design of structures.

Modeling and analysis of hysteretic structural behavior

For damaging response, the force-displacement relationship of a structure is highly nonlinear and history-dependent. For satisfactory analysis of such behavior, it is important to be able to characterize and to model the phenomenon of hysteresis accurately. A number of models have been proposed for response studies of hysteretic structures, some of which are examined in detail in this thesis. There are two popular classes of models used in the analysis of curvilinear hysteretic systems. The first is of the distributed element or assemblage type, which models the physical behavior of the system by using well-known building blocks. The second class of models is of the differential equation type, which is based on the introduction of an extra variable to describe the history dependence of the system.

Owing to their mathematical simplicity, the latter models have been used extensively for various applications in structural dynamics, most notably in the estimation of the response statistics of hysteretic systems subjected to stochastic excitation. But the fundamental characteristics of these models are still not clearly understood. A response analysis of systems using both the Distributed Element model and the differential equation model when subjected to a variety of quasi-static and dynamic loading conditions leads to the following conclusion: Caution must be exercised when employing the models belonging to the second class in structural response studies as they can produce misleading results.

The Massing's hypothesis, originally proposed for steady-state loading, can be extended to general transient loading as well, leading to considerable simplification in the analysis of the Distributed Element models. A simple, nonparametric identification technique is also outlined, by means of which an optimal model representation involving one additional state variable is determined for hysteretic systems.

On parallel computing for stochastic optimization models and algorithms

167 p.

Programming chemical kinetics: engineering dynamic reaction networks with DNA strand displacement

Over the last century, the silicon revolution has enabled us to build faster, smaller and more sophisticated computers. Today, these computers control phones, cars, satellites, assembly lines, and other electromechanical devices. Just as electrical wiring controls electromechanical devices, living organisms employ "chemical wiring" to make decisions about their environment and control physical processes. Currently, the big difference between these two substrates is that while we have the abstractions, design principles, verification and fabrication techniques in place for programming with silicon, we have no comparable understanding or expertise for programming chemistry.

In this thesis we take a small step towards the goal of learning how to systematically engineer prescribed non-equilibrium dynamical behaviors in chemical systems. We use the formalism of chemical reaction networks (CRNs), combined with mass-action kinetics, as our programming language for specifying dynamical behaviors. Leveraging the tools of nucleic acid nanotechnology (introduced in Chapter 1), we employ synthetic DNA molecules as our molecular architecture and toehold-mediated DNA strand displacement as our reaction primitive.

Abstraction, modular design and systematic fabrication can work only with well-understood and quantitatively characterized tools. Therefore, we embark on a detailed study of the "device physics" of DNA strand displacement (Chapter 2). We present a unified view of strand displacement biophysics and kinetics by studying the process at multiple levels of detail, using an intuitive model of a random walk on a 1-dimensional energy landscape, a secondary structure kinetics model with single base-pair steps, and a coarse-grained molecular model that incorporates three-dimensional geometric and steric effects. Further, we experimentally investigate the thermodynamics of three-way branch migration. Our findings are consistent with previously measured or inferred rates for hybridization, fraying, and branch migration, and provide a biophysical explanation of strand displacement kinetics. Our work paves the way for accurate modeling of strand displacement cascades, which would facilitate the simulation and construction of more complex molecular systems.

In Chapters 3 and 4, we identify and overcome the crucial experimental challenges involved in using our general DNA-based technology for engineering dynamical behaviors in the test tube. In this process, we identify important design rules that inform our choice of molecular motifs and our algorithms for designing and verifying DNA sequences for our molecular implementation. We also develop flexible molecular strategies for "tuning" our reaction rates and stoichiometries in order to compensate for unavoidable non-idealities in the molecular implementation, such as imperfectly synthesized molecules and spurious "leak" pathways that compete with desired pathways.

We successfully implement three distinct autocatalytic reactions, which we then combine into a de novo chemical oscillator. Unlike biological networks, which use sophisticated evolved molecules (like proteins) to realize such behavior, our test tube realization is the first to demonstrate that Watson-Crick base pairing interactions alone suffice for oscillatory dynamics. Since our design pipeline is general and applicable to any CRN, our experimental demonstration of a de novo chemical oscillator could enable the systematic construction of CRNs with other dynamic behaviors.

Structural dynamic eutrophication models

This article discusses problems of modelling the seasonal succession of algal species in lakes and reservoirs, and the adaptive selection of certain groups of algae in response to changes in the inputs and relative concentrations of nutrients and other environmental variables. A new generation of quantitative models is being developed which attempts to translate some important biological properties of species (survival, variation, inheritance, reproductive rates and population growth) into predictions about the survival of the fittest, where ”fitness” is measured or estimated in thermodynamic terms. The concept of ”exergy” and its calculation is explored to examine maximal exergy as a measure of fitness in ecosystems, and its use for calculating changes in species composition by means of structural dynamic models. These models accomodate short-term changes in parameters that affect the adaptive responses (species selection) of algae.

Contributions on agreement in dynamic distributed systems

139 p.

In search of climate effects on Atlantic Croaker (Micropogonias undulatus) stock off the U.S. Atlantic coast with Bayesian state-space biomass dynamic models

Atlantic Croaker (Micropogonias undulatus) production dynamics along the U.S. Atlantic coast are regulated by fishing and winter water temperature. Stakeholders for this resource have recommended investigating the effects of climate covariates in assessment models. This study used state-space biomass dynamic models without (model 1) and with (model 2) the minimum winter estuarine temperature (MWET) to examine MWET effects on Atlantic Croaker population dynamics during 1972–2008. In model 2, MWET was introduced into the intrinsic rate of population increase (r). For both models, a prior probability distribution (prior) was constructed for r or a scaling parameter (r0); imputs were the fishery removals, and fall biomass indices developed by using data from the Multispecies Bottom Trawl Survey of the Northeast Fisheries Science Center, National Marine Fisheries Service, and the Coastal Trawl Survey of the Southeast Area Monitoring and Assessment Program. Model sensitivity runs incorporated a uniform (0.01,1.5) prior for r or r0 and bycatch data from the shrimp-trawl fishery. All model variants produced similar results and therefore supported the conclusion of low risk of overfishing for the Atlantic Croaker stock in the 2000s. However, the data statistically supported only model 1 and its configuration that included the shrimp-trawl fishery bycatch. The process errors of these models showed slightly positive and significant correlations with MWET, indicating that warmer winters would enhance Atlantic Croaker biomass production. Inconclusive, somewhat conflicting results indicate that biomass dynamic models should not integrate MWET, pending, perhaps, accumulation of longer time series of the variables controlling the production dynamics of Atlantic Croaker, preferably including winter-induced estimates of Atlantic Croaker kills.

A general framework for integrating environmental time series into stock assessment models: model description, simulation testing, and example

We present a method to integrate environmental time series into stock assessment models and to test the significance of correlations between population processes and the environmental time series. Parameters that relate the environmental time series to population processes are included in the stock assessment model, and likelihood ratio tests are used to determine if the parameters improve the fit to the data significantly. Two approaches are considered to integrate the environmental relationship. In the environmental model, the population dynamics process (e.g. recruitment) is proportional to the environmental variable, whereas in the environmental model with process error it is proportional to the environmental variable, but the model allows an additional temporal variation (process error) constrained by a log-normal distribution. The methods are tested by using simulation analysis and compared to the traditional method of correlating model estimates with environmental variables outside the estimation procedure. In the traditional method, the estimates of recruitment were provided by a model that allowed the recruitment only to have a temporal variation constrained by a log-normal distribution. We illustrate the methods by applying them to test the statistical significance of the correlation between sea-surface temperature (SST) and recruitment to the snapper (Pagrus auratus) stock in the Hauraki Gulf–Bay of Plenty, New Zealand. Simulation analyses indicated that the integrated approach with additional process error is superior to the traditional method of correlating model estimates with environmental variables outside the estimation procedure. The results suggest that, for the snapper stock, recruitment is positively correlated with SST at the time of spawning.