Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

Seismic performance of hybrid fiber reinforced polymer-concrete pier frame systems

As an alternative to transverse spiral or hoop steel reinforcement, fiber reinforced polymers (FRPs) were introduced to the construction industry in the 1980’s. The concept of concrete-filled FRP tube (CFFT) has raised great interest amongst researchers in the last decade. FRP tube can act as a pour form, protective jacket, and shear and flexural reinforcement for concrete. However, seismic performance of CFFT bridge substructure has not yet been fully investigated. Experimental work in this study included four two-column bent tests, several component tests and coupon tests. Four 1/6-scale bridge pier frames, consisting of a control reinforced concrete frame (RCF), glass FRP-concrete frame (GFF), carbon FRP-concrete frame (CFF), and hybrid glass/carbon FRP-concrete frame (HFF) were tested under reverse cyclic lateral loading with constant axial loads. Specimen GFF did not show any sign of cracking at a drift ratio as high as 15% with considerable loading capacity, whereas Specimen CFF showed that lowest ductility with similar load capacity as in Specimen GFF. FRP-concrete columns and pier cap beams were then cut from the pier frame specimens, and were tested again in three point flexure under monotonic loading with no axial load. The tests indicated that bonding between FRP and concrete and yielding of steel both affect the flexural strength and ductility of the components. The coupon tests were carried out to establish the tensile strength and elastic modulus of each FRP tube and the FRP mold for the pier cap beam in the two principle directions of loading. A nonlinear analytical model was developed to predict the load-deflection responses of the pier frames. The model was validated against test results. Subsequently, a parametric study was conducted with variables such as frame height to span ratio, steel reinforcement ratio, FRP tube thickness, axial force, and compressive strength of concrete. A typical bridge was also simulated under three different ground acceleration records and damping ratios. Based on the analytical damage index, the RCF bridge was most severely damaged, whereas the GFF bridge only suffered minor repairable damages. Damping ratio was shown to have a pronounced effect on FRP-concrete bridges, just the same as in conventional bridges. This research was part of a multi-university project, which is founded by the National Science Foundation (NSF) - Network for Earthquake Engineering Simulation Research (NEESR) program.

Seismic Performance of Hybrid Fiber Reinforced Polymer-Concrete Pier Frame Systems

As an alternative to transverse spiral or hoop steel reinforcement, fiber reinforced polymers (FRPs) were introduced to the construction industry in the 1980's. The concept of concrete-filled FRP tube (CFFT) has raised great interest amongst researchers in the last decade. FRP tube can act as a pour form, protective jacket, and shear and flexural reinforcement for concrete. However, seismic performance of CFFT bridge substructure has not yet been fully investigated. Experimental work in this study included four two-column bent tests, several component tests and coupon tests. Four 1/6-scale bridge pier frames, consisting of a control reinforced concrete frame (RCF), glass FRP-concrete frame (GFF), carbon FRP-concrete frame (CFF), and hybrid glass/carbon FRP-concrete frame (HFF) were tested under reverse cyclic lateral loading with constant axial loads. Specimen GFF did not show any sign of cracking at a drift ratio as high as 15% with considerable loading capacity, whereas Specimen CFF showed that lowest ductility with similar load capacity as in Specimen GFF. FRP-concrete columns and pier cap beams were then cut from the pier frame specimens, and were tested again in three point flexure under monotonic loading with no axial load. The tests indicated that bonding between FRP and concrete and yielding of steel both affect the flexural strength and ductility of the components. The coupon tests were carried out to establish the tensile strength and elastic modulus of each FRP tube and the FRP mold for the pier cap beam in the two principle directions of loading. A nonlinear analytical model was developed to predict the load-deflection responses of the pier frames. The model was validated against test results. Subsequently, a parametric study was conducted with variables such as frame height to span ratio, steel reinforcement ratio, FRP tube thickness, axial force, and compressive strength of concrete. A typical bridge was also simulated under three different ground acceleration records and damping ratios. Based on the analytical damage index, the RCF bridge was most severely damaged, whereas the GFF bridge only suffered minor repairable damages. Damping ratio was shown to have a pronounced effect on FRP-concrete bridges, just the same as in conventional bridges. This research was part of a multi-university project, which is founded by the National Science Foundation (NSF) Network for Earthquake Engineering Simulation Research (NEESR) program.