Franklin Y. Cheng

Optimal placement of controllers for seismic structures

Abstract Active control devices can be implemented on seismic structures to reduce structural response from earthquakes. Certain locations of the structure are advantageous for placement of the controllers in the sense that these locations effectively reduce structural response while using the minimum control effort. A method is proposed which uses an empirical procedure to find the optimal locations by maximizing an optimal locations index. The method takes into consideration the modal responses and earthquake spectra for two different earthquake records. The proposed method is compared to two methods; in the first method a control energy performance index is minimized; the second method uses a minimum response performance index as the criterion. The proposed method is found to agree with the two alternative methods and saves computation time.

Experimental Characterization of Piezoelectric Friction Dampers

A piezoelectric friction damper was designed and fabricated to control the 1/4-scale, three-story frame structure in the Structures Laboratory at the University of Missouri-Rolla. In this paper, the damper is characterized in terms of energy dissipation, frequency and temperature dependence, and long-term durability under harmonic loading.

Optimum control of a hybrid system for seismic excitations with state observer technique

This paper presents a theoretical study of a hybrid seismic response control system comprising a passive fluid viscous damper and an active control system with a hydraulic actuator and acceleration sensors. The analytical model of this system is derived in the discrete time domain with actuator and damper dynamics considered. Based on digital control theory, a state observer is established for optimal control strategies of the hybrid system. This study shows that the hybrid system gains the advantages of both active and passive control techniques currently in vogue; and that, with the state observer technique, a seismic response control system is more effective and less complicated because full-state feedback seismic control algorithms can be implemented by means of acceleration sensors, and a smaller number of sensors is required. A numerical simulation for seismic response of a building structure with a hybrid control system is presented to demonstrate the effectiveness of this control strategy for the hybrid system.

MULTIOBJECTIVE OPTIMIZATION OF SEISMIC STRUCTURES

This paper presents a constrained multiobjective optimization method in the form of a robust, practical, problem-independent formulation based on genetic algorithm combined with game theory, and investigates the effect of multiobjective optimiztion on structural design. The study includes objectives, constraints, and design variables as well as their effect on structural design and behavior. The algorithm comprises – multiobjective fitness function, niche method, and Pareto set filter. A 10-story setback building is used to illustrate the evaluation of three choices: steel frame, reinforced concrete frame, composite steel and reinforced concrete frame. Evaluation is based on economics as well as performance. Comparison of optimum design results is obtained with consideration of weight, structural cost, and seismic energy for all three frames subjected to the same seismic input. Constraints are based on Uniform Building Code specifications including stress, displacement, drift, and ratio of story stiffness. The new approach provides a powerful tool to locate a global solution. Overview of Multioptimization Problemsolving In this research, game theory, fuzzy set theory, and Pareto genetic algorithm are applied to multiobjective optimization programming, constraint space transformation, and generation of nondominated sets. Game theory can find a compromise solution which satisfies all competing objectives in a cooperative game for a multiobjective optimization problem. Using fuzzy set theory can transform a constrained optimization problem into a nonconstrained one which can be optimized by a genetic algorithm. Pareto GA can generate a nondominated set even for

Generalised optimal active control algorithm for seismic-resistant structures with active and hybrid control

The paper presents several optimal control algorithms including Riccati and instantaneous algorithms (ROAC and IOAC), generalised optimal control algorithm (GOAC), along with state control and state-slope control gain matrices. The strength and weaknesses of these algorithms are assessed and illustrated with numerical examples. It is concluded that GOAC is better than ROAC and IOAC in performance and that hybrid control is more effective in reducing structural response than active or passive devices only. Selection of state control or state-slope control gain matrix depends on the characteristics of the passive device.

Inelastic analysis of 3-D mixed steel and reinforced concrete seismic building systems

Abstract This paper presents partial results of a NSF research project for studying the response behavior of inelastic building systems subjected to the simultaneous input of static loads and multicomponent earthquake motions that can be applied in any direction of the structural plan. The analysis includes the secondorder moment resulting from the gravity load and the vertical ground motion. The building systems may have elevator cores, floor diaphragms, and shear walls of reinforced concrete as well as steel beams, columns, and bracings. The material behavior of the steel members is based on the Ramberg-Osgood hysteresis loop with the consideration of the Bauschinger effect. Takedas model is employed for the reinforced concrete elements. The system stiffness and geometric matrices, and the numerical integration procedures are developed consistantly with the building characteristics that each floor has dynamic degrees of freedom associated with the axial displacements of the columns and one torsional and two transverse displacements at the mass center. Thus, computation efficiency can be achieved by eliminating structural joint rotations from floor to floor with only the displacements associated with the lumped masses left for the motion equation. The yielding surface of a steel member is based on the nonlinear interactions and the von Mises yield criterion. A computer program, INRESB-3D, has been developed for the inelastic response behavior of (1) the transverse, vertical and torsional movements of a structure; (2) the internal moments and their associated rotations of the members; (3) the energy absorption characteristics of a structure; and (4) the requirement of the ductility factors and the excursion ratios of various building systems. Included in the paper is an example of unsymmetric eight-story building with steel columns and a concrete wall.

Robust control of seismic structures using independent modal-space techniques

Active robust structural controls have been utilized in the control of aerospace structures for many years but they have only been recently investigated in the context of control for civil engineering structures. The results of an investigation of the utilization of these methods on building-like structures are presented in this paper. The closed-loop systems take into account the limited available actuation force and are inherently insensitive to parameter variations and modeling uncertainties. Independent modal-space control (IMSC) is a structural control technique where the multi-input-multi-output configuration-space system is transformed into a set of uncoupled single-input-single-output modal-space systems. A modal controller is designed for each modal-space system and the set of modal controllers is transformed back into configuration-space. By combining IMSC with robust control techniques such as LQG/LTR or H(infinity ), a robust structural control design technique is proposed in this paper. Robust IMSC techniques are employed for control of seismic structures where a small number of actuators are used to control the first few modes of the structure. We have designed and implemented robust IMSC controllers on an experimental building-like structure. This structure utilizes torque motor driven active tendons as actuators and rests on a shaking table which is capable of providing one dimensional base excitation similar to earthquake ground motion. A three input-three output model of the structure, including the torque motor actuators, was developed using experimental data. The experimental structural identification technique, based on standard modal analysis methods, provides the mathematical model that describes the behavior of the structure. An H(infinity ) based IMSC controller has been designed and implemented on this structure using a dSPACE control development system. The results show that the performance of the system is satisfactory in the presence of unmodeled dynamics, parameter variations, and disturbance inputs.

MULTIOBJECTIVE OPTIMUM DESIGN OF STRUCTURES WITH GENETIC ALGORITHM AND GAME THEORY: APPLICATION TO LIFE-CYCLE COST DESIGN

ABSTRACT Loss of life and property from possible future earthquakes as well as the expense and difficulty of post-earthquake rehabilitation and reconstruction strongly suggest the need for proper structural design with damage control. Design criteria should balance initial cost of the structure with expected losses from potential earthquake-induced structural damage. Life-cycle cost design addresses these issues. Such a design methodology can be developed using multiobjective and multilevel optimization techniques. Presentation here focuses on genetic algorithm and game theory as well as a life-cycle cost model for this innovative design methodology. Genetic algorithms (GAs) have the characteristic of maintaining a population of solutions, and can search in a parallel manner for many nondominated solutions. These features coincide with the requirement of seeking a Pareto optimal set in a multiobjective optimization problem. The rationale for multiobjective optimization via GAs is that at each generation, the fitness of each individual is defined according to its nondominated property. Since nondominated individuals are assigned the highest fitness values, the convergence of a population will go to the nondominated zone – the Pareto optimal set. Based on this concept, a Pareto GA whose goal is to locate the Pareto optimal set of a multiobjective optimization problem is developed. In this GA, to avoid missing Pareto optimal points during evolutionary processes, a new concept called Pareto-set filter is adopted. At each generation, the points of rank 1 are put into the filter and undergo a nondominated check. In addition, a niche technique is provided to prevent genetic drift in population evolution. This technique sets a replacement rule for reproduction procedures. For a constrained optimization problem, a revised penalty function method is introduced to transfer a constrained problem into a nonconstrained one. The transferred function of a point contains information on a points status (feasible or infeasible), position in a search region, and distance to the Pareto optimal set. Three numerical examples are provided: 1) optimum design of a seismic-resistant structure with/without control, 2) optimum design for a final structural system selected from steel frame, reinforced concrete, or composite system, and 3) sensitivity analysis of the effect of cost function on structural probability failure. It is concluded that multiobjective and multilevel optimization is essential to determine target reliability and seismic building code performance.