Optimal Design of Nonlinear Viscous Dampers for Protection of Isolated Bridges

A probabilistic framework based on stochastic simulation is presented in this chapter for optimal design of supplemental dampers for multi - span bridge systems supported on abutments and intermediate piers through isolation bearings. The bridge model explicitly addresses nonlinear characteristics of the isolators and the dampers, the dynamic behavior of the abutments, and the effect of pounding between the neighboring spans to each other as well as to the abutments. A probabilistic framework is used to address the various sources of structural and excitation uncertainties and characterize the seismic risk for the bridge. Stochastic simulation is utilized for evaluating this seismic risk and performing the associated optimization when selecting the most favorable damper characteristics. An illustrative example is presented that considers the design of nonlinear viscous dampers for protection of a two-span bridge.

Optimal Performance-Based Seismic Design

In this chapter, the reader gets acquainted with the philosophy of performance-based design, its principles, and an overview of the procedures for performance evaluation of structures. The essential prerequisites of optimal performance-based design, including nonlinear analysis, optimization algorithms, and nonlinear sensitivity analysis, are introduced. The methods of nonlinear analysis and optimization are briefly presented, and the formulation of optimal performance-based design with emphasis on deterministic type, rather than probabilistic- (or reliability)-based formulation is discussed in detail. It is revealed how real performance-based design is tied to optimization, and the reason is given for why, without optimization algorithms, multilevel performance-based design is almost impossible.

Performance-Based Seismic Design

An approach is presented to structural optimization for performance-based design in earthquake engineering. The objective is the minimization of the total cost, including repairing damage produced by future earthquakes, and satisfying minimum target reliabilities in three performance levels (operational, life safety, and collapse). The different aspects of the method are considered: a nonlinear dynamic structural analysis to obtain responses for a set of earthquake records, representing these responses with neural networks, formulating limit-state functions in terms of deformations and damage, calculating achieved reliabilities to verify constraint violations, and the development of a gradient-free optimization algorithm. Two examples illustrate the methodology: 1) a reinforced concrete portal for which the design parameters are member dimensions and steel reinforcement ratios, and 2) optimization of the mass at the cap of a pile, to meet target reliabilities for two levels of cap displacement. The objective of this latter example is to illustrate model effects on optimization, using two different hysteresis approaches.

Health Assessment of Engineering Structures Using Graphical Models

A hybrid qualitative-quantitative health assessment of structures using the bond graph theory is presented in this chapter. Bond graph (BG) is an energy-based graphical-modeling tool for physical dynamic systems, actuators, and sensors. BG provides domain-independent framework for modeling dynamic systems with interacting components from multiple domains. Discrete structures are modeled using one-to-one bond graph elements, while continuous structures are modeled using finite-mode bond graphs. BG facilitates the construction of temporal causal graph (TCG) that links the system response to the damaged component or faulty sensor. TCG provides qualitative damage isolation, which is not possible using most existing system identification techniques. This leads to rapid isolation of damage and significant reduction in computations. Quantitative identification of damage size is performed by analyzing the substructure containing the damaged component, using the nonlinear least-squares optimization technique, thus reducing the computations. The health assessment algorithm developed in this chapter combines the Generic Modeling Environment (GME), the Fault Adaptive Control Technology (FACT) software, and Matlab Simulink®. Numerical illustrations on BG modeling of a hydraulic actuator and system identification of a fifteen-story shear building and a high-rise structure under earthquake loads are provided.

Fuzzy Identification of Seismically Excited Smart Systems

In this chapter, a nonlinear modeling framework to identify nonlinear behavior of smart structural systems under seismic excitations is proposed. To this end, multi-input-multi-output (MIMO) autoregressive exogenous (ARX) input models and Takagi-Sugeno (TS) fuzzy models are coalesced as the MIMO ARX-TS fuzzy model. The premised part of the proposed MIMO ARX-TS fuzzy model is optimized using the hierarchical clustering (HRC) algorithm, while its consequent parameters are optimized via the weighted linear least squares estimation. The performance of the proposed model is investigated using the dynamic response of a three-story shear planer frame structure equipped with a magnetorheological (MR) damper subject to earthquake disturbances. Furthermore, the impact of the HRC algorithm on the performance of the MIMO ARX-TS fuzzy model is compared with that of the subtractive and the fuzzy C-means clustering algorithms. The equivalence of the original and identified data is numerically shown to prove that the HRC MIMO ARX-TS fuzzy model introduced here is effective in estimating nonlinear behavior of a seismically excited building-MR damper system.

Metaheuristic Optimization in Seismic Structural Design and Inspection Scheduling of Buildings

Optimization is a field where extensive research has been conducted over the last decades. Many types of problems have been addressed, and many types of algorithms have been developed, while their range of applications is continuously growing. The chapter is divided into two parts; in the first part, the life-cycle cost analysis is used as an assessment tool for designs obtained by means of prescriptive and performance-based optimum design methodologies. The prescriptive designs are obtained through a single-objective formulation, where the initial construction cost is the objective to be minimized, while the performance-based designs are obtained through a two-objective formulation where the life-cycle cost is considered as an additional objective also to be minimized. In the second part of the chapter, the problem of inspection of structures and routing of the inspection crews following an earthquake in densely populated metropolitan areas is studied. A model is proposed and a decision support system is developed to aid local authorities in optimally assigning inspectors to critical infrastructures. A combined particle swarm – ant colony optimization based framework is implemented, which proves to be an instance of a successful application of the philosophy of bounded rationality and decentralized decision-making for solving global optimization problems.

Damage Assessment of Inelastic Structures under Simulated Critical Earthquakes

Damage of structures can be significantly reduced through robust prediction of possible future earthquakes that can occur during the life-time of the structure and through accurate modeling of the nonlinear behavior of the structure under seismic loads. Modern seismic codes specify natural records and artificially generated ground accelerations as input to the nonlinear time-history analysis of the structure. The advantage of using natural records is the inclusion of all important characteristics of the ground motion (fault properties, path effects and local soil condition) in the design input. This option requires selecting and scaling a set of proper accelerograms from the available records. However, the site under consideration may have limited or scarce earthquake data. In such case, numerically simulated ground motions can be employed as input to the dynamic analysis of the structure. This chapter deals with the damage assessment of inelastic structures under numerically simulated critical earthquakes using nonlinear optimization, inelastic time-history analysis, and damage indices.

Applications of Topology Optimization Techniques in Seismic Design of Structure

During the last two decades, topology optimization techniques have been successfully applied to a wide range of problems including seismic design of structures. This chapter aims to provide an introduction to the topology optimization methods and a review of the applications of these methods in earthquake engineering. Two well-established topology optimization techniques are introduced. Several problems including eigenfrequency control of structures, compliance minimization under periodic loading, and maximizing energy absorption of passive dampers will be addressed. Numerical instabilities and approaches to overcome them will be discussed. The application of the presented approaches and methods will be illustrated using numerical examples. It will be shown that in seismic design of structures, topology optimization methods can be useful in providing conceptual design for structural systems as well as detailed design of structural members.

Overall Conceptual Seismic Design and Local Seismic Capacity Design for Components of Bridges

From the perspective of “overall conceptual seismic design,” four design strategies are presented to decrease and balance the seismic force and displacement demands for some bridges working in a linear and elastic state: the adjustment of the layout and detail of piers and expansion joints for a typical long span continuous girder bridge, the adoption of a new-type spatial bridge tower for a long span cable-stayed bridge, the study on the isolation mechanism of an elastic cable seismic isolation device for another cable-stayed bridge, and the study on the seismic potential and performance for long span SCC (steel-concrete composite) bridges. From the perspective of “local seismic capacity design,” three earthquake resistant strategies are presented to achieve economical, applicable, and valid seismic design of local components of bridges working in a nonlinear state: the adoption and the study on a new cable sliding friction aseismic bearing, the study on the seismic capacities of single-column bridge piers wholly and locally reinforced with steel fiber reinforced concrete (SFRC), the study on the seismic capacities, and the hysteretic performance and energy dissipation capabilities of bridge pile group foundations strengthened with the steel protective pipes (SPPs). Research results show that these seismic design strategies are effective to improve the seismic performance of bridges.

Efficient Robust Optimization of Structures Subjected to Earthquake Load and Characterized by Uncertain Bounded System Parameters

An efficient robust design optimization (RDO) procedure is proposed in the framework of an adaptive response surface method (RSM) for structures subjected to earthquake load and characterized by uncertain but bounded system parameters. The basic idea of the proposed RDO approach is to improve the robustness of a design by using a new dispersion index which utilizes the relative importance of the gradients of the performance function. The same concept is also applied to the constraints. The repeated computations of stochastic responses and their sensitivities for evaluating the stochastic constraint of the associated optimization problem are efficiently obtained in the framework of an adaptive RSM. The proposed RDO approach is elucidated through the optimization of a three-storied concrete frame structure. The numerical study depicts that the proposed RDO results are in conformity with the conventional RDO results. However, definite improvements are achieved in terms of robustness and computational time requirements indicating its efficiency over the conventional RDO approach.