Updating of Finite Element Models using static and dynamic optical strains with application to damage assessment

In the recent years, vibration-based structural damage identification has been subject of significant research in structural engineering. The basic idea of vibration-based methods is that damage induces mechanical properties changes that cause anomalies in the dynamic response of the structure, which measures allow to localize damage and its extension. Vibration measured data, such as frequencies and mode shapes, can be used in the Finite Element Model Updating in order to adjust structural parameters sensible at damage (e.g. Young’s Modulus). The novel aspect of this thesis is the introduction into the objective function of accurate measures of strains mode shapes, evaluated through FBG sensors. After a review of the relevant literature, the case of study, i.e. an irregular prestressed concrete beam destined for roofing of industrial structures, will be presented. The mathematical model was built through FE models, studying static and dynamic behaviour of the element. Another analytical model was developed, based on the ‘Ritz method’, in order to investigate the possible interaction between the RC beam and the steel supporting table used for testing. Experimental data, recorded through the contemporary use of different measurement techniques (optical fibers, accelerometers, LVDTs) were compared whit theoretical data, allowing to detect the best model, for which have been outlined the settings for the updating procedure.

Substructuring approache in state space models for dynamic system parameters identification

In the recent decade, the request for structural health monitoring expertise increased exponentially in the United States. The aging issues that most of the transportation structures are experiencing can put in serious jeopardy the economic system of a region as well as of a country. At the same time, the monitoring of structures is a central topic of discussion in Europe, where the preservation of historical buildings has been addressed over the last four centuries. More recently, various concerns arose about security performance of civil structures after tragic events such the 9/11 or the 2011 Japan earthquake: engineers looks for a design able to resist exceptional loadings due to earthquakes, hurricanes and terrorist attacks. After events of such a kind, the assessment of the remaining life of the structure is at least as important as the initial performance design. Consequently, it appears very clear that the introduction of reliable and accessible damage assessment techniques is crucial for the localization of issues and for a correct and immediate rehabilitation. The System Identification is a branch of the more general Control Theory. In Civil Engineering, this field addresses the techniques needed to find mechanical characteristics as the stiffness or the mass starting from the signals captured by sensors. The objective of the Dynamic Structural Identification (DSI) is to define, starting from experimental measurements, the modal fundamental parameters of a generic structure in order to characterize, via a mathematical model, the dynamic behavior. The knowledge of these parameters is helpful in the Model Updating procedure, that permits to define corrected theoretical models through experimental validation. The main aim of this technique is to minimize the differences between the theoretical model results and in situ measurements of dynamic data. Therefore, the new model becomes a very effective control practice when it comes to rehabilitation of structures or damage assessment. The instrumentation of a whole structure is an unfeasible procedure sometimes because of the high cost involved or, sometimes, because it’s not possible to physically reach each point of the structure. Therefore, numerous scholars have been trying to address this problem. In general two are the main involved methods. Since the limited number of sensors, in a first case, it’s possible to gather time histories only for some locations, then to move the instruments to another location and replay the procedure. Otherwise, if the number of sensors is enough and the structure does not present a complicate geometry, it’s usually sufficient to detect only the principal first modes. This two problems are well presented in the works of Balsamo [1] for the application to a simple system and Jun [2] for the analysis of system with a limited number of sensors. Once the system identification has been carried, it is possible to access the actual system characteristics. A frequent practice is to create an updated FEM model and assess whether the structure fulfills or not the requested functions. Once again the objective of this work is to present a general methodology to analyze big structure using a limited number of instrumentation and at the same time, obtaining the most information about an identified structure without recalling methodologies of difficult interpretation. A general framework of the state space identification procedure via OKID/ERA algorithm is developed and implemented in Matlab. Then, some simple examples are proposed to highlight the principal characteristics and advantage of this methodology. A new algebraic manipulation for a prolific use of substructuring results is developed and implemented.

Pushover analysis of an existing reinforced concrete bridge:Jamboree Road Overcrossing in Irvine, California

The work for the present thesis started in California, during my semester as an exchange student overseas. California is known worldwide for its seismicity and its effort in the earthquake engineering research field. For this reason, I immediately found interesting the Structural Dynamics Professor, Maria Q. Feng's proposal, to work on a pushover analysis of the existing Jamboree Road Overcrossing bridge. Concrete is a popular building material in California, and for the most part, it serves its functions well. However, concrete is inherently brittle and performs poorly during earthquakes if not reinforced properly. The San Fernando Earthquake of 1971 dramatically demonstrated this characteristic. Shortly thereafter, code writers revised the design provisions for new concrete buildings so to provide adequate ductility to resist strong ground shaking. There remain, nonetheless, millions of square feet of non-ductile concrete buildings in California. The purpose of this work is to perform a Pushover Analysis and compare the results with those of a Nonlinear Time-History Analysis of an existing bridge, located in Southern California. The analyses have been executed through the software OpenSees, the Open System for Earthquake Engineering Simulation. The bridge Jamboree Road Overcrossing is classified as a Standard Ordinary Bridge. In fact, the JRO is a typical three-span continuous cast-in-place prestressed post-tension box-girder. The total length of the bridge is 366 ft., and the height of the two bents are respectively 26,41 ft. and 28,41 ft.. Both the Pushover Analysis and the Nonlinear Time-History Analysis require the use of a model that takes into account for the nonlinearities of the system. In fact, in order to execute nonlinear analyses of highway bridges it is essential to incorporate an accurate model of the material behavior. It has been observed that, after the occurrence of destructive earthquakes, one of the most damaged elements on highway bridges is a column. To evaluate the performance of bridge columns during seismic events an adequate model of the column must be incorporated. Part of the work of the present thesis is, in fact, dedicated to the modeling of bents. Different types of nonlinear element have been studied and modeled, with emphasis on the plasticity zone length determination and location. Furthermore, different models for concrete and steel materials have been considered, and the selection of the parameters that define the constitutive laws of the different materials have been accurate. The work is structured into four chapters, to follow a brief overview of the content. The first chapter introduces the concepts related to capacity design, as the actual philosophy of seismic design. Furthermore, nonlinear analyses both static, pushover, and dynamic, time-history, are presented. The final paragraph concludes with a short description on how to determine the seismic demand at a specific site, according to the latest design criteria in California. The second chapter deals with the formulation of force-based finite elements and the issues regarding the objectivity of the response in nonlinear field. Both concentrated and distributed plasticity elements are discussed into detail. The third chapter presents the existing structure, the software used OpenSees, and the modeling assumptions and issues. The creation of the nonlinear model represents a central part in this work. Nonlinear material constitutive laws, for concrete and reinforcing steel, are discussed into detail; as well as the different scenarios employed in the columns modeling. Finally, the results of the pushover analysis are presented in chapter four. Capacity curves are examined for the different model scenarios used, and failure modes of concrete and steel are discussed. Capacity curve is converted into capacity spectrum and intersected with the design spectrum. In the last paragraph, the results of nonlinear time-history analyses are compared to those of pushover analysis.

Influence of cladding on robustness of multi-storey buildings

In this dissertation the influence of a precast concrete cladding system on structural robustness of a multi-storey steel-composite building is studied. The analysis follows the well-established framework developed at Imperial College London for the appraisal of robustness of multi-storey buildings. For this scope a simplified nonlinear model of a typical precast concrete façade-system is developed. Particular attention is given to the connection system between structural frame and panel, recognised as the driving component of the nonlinear behaviour of the façade-system. Only connections involved in the gravity load path are evaluated (bearing connections). Together with standard connection, a newly proposed system (Slotted Bearing Connection) is designed to achieve a more ductile behaviour of the panel-connection system. A parametric study involving the dimensions of panel-connection components is developed to search for an optimal configuration of the bearing connection. From the appraisal of structural robustness of the panelised frame it is found that the standard connection systems may reduce the robustness of a multi-storey frame due to a poor ductile behaviour while the newly proposed connection is able to guarantee an enhanced response to the panelised multi-storey frame thanks to a higher ductility.

Stochastic local volatility model for fx markets

Questa tesi verte sullo studio di un modello a volatilità stocastica e locale, utilizzato per valutare opzioni esotiche nei mercati dei cambio. La difficoltà nell'implementare un modello di tal tipo risiede nella calibrazione della leverage surface e uno degli scopi principali di questo lavoro è quello di mostrarne la procedura.

Regularization methods for the solution of a nonlinear least-squares problem in tomography

In this work we study a polyenergetic and multimaterial model for the breast image reconstruction in Digital Tomosynthesis, taking into consideration the variety of the materials forming the object and the polyenergetic nature of the X-rays beam. The modelling of the problem leads to the resolution of a high-dimensional nonlinear least-squares problem that, due to its nature of inverse ill-posed problem, needs some kind of regularization. We test two main classes of methods: the Levenberg-Marquardt method (together with the Conjugate Gradient method for the computation of the descent direction) and two limited-memory BFGS-like methods (L-BFGS). We perform some experiments for different values of the regularization parameter (constant or varying at each iteration), tolerances and stop conditions. Finally, we analyse the performance of the several methods comparing relative errors, iterations number, times and the qualities of the reconstructed images.

Boundary condition identification of a bridge pier using experimental data and FEM modal updating

Over the past twenty years, new technologies have required an increasing use of mathematical models in order to understand better the structural behavior: finite element method is the one mostly used. However, the reliability of this method applied to different situations has to be tried each time. Since it is not possible to completely model the reality, different hypothesis must be done: these are the main problems of FE modeling. The following work deals with this problem and tries to figure out a way to identify some of the unknown main parameters of a structure. This main research focuses on a particular path of study and development, but the same concepts can be applied to other objects of research. The main purpose of this work is the identification of unknown boundary conditions of a bridge pier using the data acquired experimentally with field tests and a FEM modal updating process. This work doesn’t want to be new, neither innovative. A lot of work has been done during the past years on this main problem and many solutions have been shown and published. This thesis just want to rework some of the main aspects of the structural optimization process, using a real structure as fitting model.