Depreme dayanıklı yapı tasarımında aktif kontrolünün kullanılması
Active control for earthauake resistant structural design
- Tez No: 39708
- Danışmanlar: PROF.DR. MEHMET BAKİOĞLU
- Tez Türü: Yüksek Lisans
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Aktif denetim, Bina bilgisi, Deprem, Active control, Building information, Earthquake
- Yıl: 1994
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Bu çalışmada benzetilmiş deprem ve gerçek deprem kayıtları kullanılarak nonlineer yapıların aktif kontrol altında davranışları incelenmiştir. Kontrol algoritması olarak 1987'de Yang J. tarafından nonlineer yapılar için geliştirilen kapalı- çevrim, açık-çevrim ve kapalı-açık çevrim ani optimal kontrol algoritmalarından ani optimal kapalı-çevrim kontrol algoritması kullanılmıştır. Ani optimal kontrol algoritmalarında, kontrol vektörü u(t) ve yapı mukabele vektörü z(t)'ye göre kuadratik olarak seçilen J performans indeksi her t anında minimize edilmektedir. Nonlineer hareket denklemlerinin çözümünde Wilson-e metodu kullanılmıştır. Aktif kontrolün yapı davranışına etkisini araştırmak için 3 sayısal örnek çözülmüştür. Birinci sayısal örnekte benzetilmiş^ deprem, Kanai-Tajimi güç spektrum fonksiyonu kullanılarak stasyoner olmayan rastgele işlem olarak modellenmiştir. İkinci örnekte 1992 Erzincan depremi, üçüncü örnekte ise Elcentro depremi kullanılmıştır. Birinci ve üçüncü örnekte, tüm yapı mukabelesinin elastik bölgede kaldığı görülmüştür. Fakat ikinci örnekde, aktif kütle sönümleyicisine yakın katların mukabelesi elastik bölgede kalırken, alt katların mukabelesinin elastik bölge dışına çıktığı görülmüştür. Bu neticeyi etkileyen en önemli faktör Q ve R matrislerine atanan değerlerdir. Dolayısıyla Q ve R ağırlık matrislerine atanan değerlere bağlı olarak yapı davranışını elastik bölgede tutmak mümkündür. Fakat bunu garanti altına almak için Q ve R matrislerinin sabit olmayıp, her t anında ölçülüp geri beslenen yapı mukabelesine göre zamanla değişebilen matrisler olmaları gerekmektedir. Bu konuda çalışmalar devam etmektedir. Bu çalışmada ayrıca geniş bir kaynak taraması yapılmıştır. Aktif kontrolün inşaat mühendisliğindeki uygulamaları ile ilgili kaynaklar EK D' de verilmiştir.
Özet (Çeviri)
SUMMARY ACTIVE CONTROL FOR EARTHQUAKE-RESISTANT STRUCTURAL DESIGN In structural engineering,“active structural control”has become an area of research in which the motion of structure is controlled or modified using a control system through some external enrgy supply. Due to following motivating factors, there has been a flurry of research activities in the area of active control of civil engineering structures. 1. In last 20 years, due to trend toward taller, more flexible and longer structures, under large environmental loads such as strong winds and large eartquakes excessive vibrational levels could be reached which result in adversely affecting human comfort and even structural safety. The application of active control is one of the options of protecting such structures agains excessive vibrations. 2. Active or hybrid active-passive systems can be attractive choices for retrofitting or strengthening existing structures against earthquake hazards. Using interior shear walls or base isolation systems are structurally invasive. But, active systems can be more effective and can be incorporated into an existing structure with less interference. 3. In conventional earthquake resistant design, most structures are designed to withstand earthquakes of moderate intensity elastically, and to prevent a collapse during a severe earthquake, thereby preventing loss of human life. However, in many urban areas not only individual buildings, but also entire city functions are becoming intelligence oriented. Therefore, it seems unwise to cling to a design philosophy designated for the severe earthquakes, in which a barely prevented collapse at the structural ultimate limit is recognized as acceptable, providing there is no loss of human life. VIIs such thinking still acceptable? The conventional philosophy, which is several decades old, can result in a decrease in an individual building's function and loss in its financial value, and prevent reuse of the building after severe earthquakes. This should be tolarated in the coming age. A technolog, is required that will not only suppress the vibrations of buildings, but will preserve the information and communication function that sustains a city's life. 4. Civil Engineering structures are not designated to withstand all possible external loads. However, extraordinar excessive loading may occur, resulting in structural failur. So, active control can mean a last resort attempt to save a structure which would not be able to survive. When we consider the high cost of some recent large structures such as deep-water offshore platforms, active control seems to be particularly attractive. 5. Some structures house valuable and sensitive equipment. Their operating safety is of great importance. Thus, to ensure proper operating conditions for such sensitive equipments, active control can be applied at the substructure level. 6. Even though passive control devices such as base isolation systems, tuned mass dampers, viscoelastic dampers installed in some existing structures result in good performance, they have important inherent limitations. For example, a tuned mass damper can only be effective at the vibration mode at which it is tuned. But, an active mass damper can be effective over a much wider frequency range. 7. Since active control elevates structural concepts from a static and passive level to one of dynamicism and adaptabilitiy, it is not only attractive, but potentially revolutionary. Here, we should emphasise that the basic concepts of active control are not new. They have been used as the main tools of electrical and control engineering for many decades. But, even though much of the theoretical basis is in modern control theory, application of contol theories to civil engineering structures is unique in many ways. An active structural control system consists of the following 3 basic parts. vii1. Sensors located about the structure to measure either external excitations, or structural response variables, or both. 2. Devices to process the measured information and to compute necessary control forces needed based on. a given control algorithm. 3. Actuators, usually powered by external energy sources, to produce the required forces. When only the structural response variables are measured, the control configuration is referred to as closed-loop control since the structural response is continually monitored and this information is used to mate continual corrections to the applied control forces. An open-looped control results when the control forces are regulated only by the measured excitations. In case where the information on both the response quantities and excitation are utilized for control design, the term open-closed loop control is used in the literature. In classical optimal control standart quadratic performance index rtf J=\ [ZT(t)QZ(t)+UT(t)RU(t)]dt is used. Jo tf is a duration defined to be longer than that of the earthquake. Q and R are weighting matrices. In classical optimal closed-loop control, Riccati matrix P(t) does not correspond to the optimal closed-loop control for earthquake-excited building structure. Because it is obtained by setting the ground acceleration X0(t) to zero. So, the optimal closed-loop control is achieved by the Ricati matrix only if the earthquake excitation is either zero or a white noise random process. While the classical optimal open-loop control and the optimal closed-open loop control are superior to the Riccati closed-loop control, they are alson not applicable to earthquake-excited structures. Because, in these algorithms unknown vector q(t) should be solved backwards from the terminal time tf, indicating that the entire earthquake accelaration history X0(t) should be known a priori. Although the earthquake acceleration X0(t) is measurable, it is a random process and it is not known a priori. There are other applicable closed-loop control algorithms that are not optimal, such as the methods of pole assignment. The pole assignment method is tedious for complex building structures with many degrees of freedom, and it is not clear where the poles (eigenvalues) of the structures should be assigned. viiiBecause earthquake excitation is a random process, and it is not known a priori. While the earthquake ground motion is not known a priori, the base excitation of the building can be measured“real time”on-line by installing sensors on the basement floor. In other words, at any particular time t, the base excitation record is available up to that time instant t. That type of important information has been used in the development of instantaneous optimal control algorithms. The reason why it is not feasible to apply the classical optimal open-loop or closed-open-loop control algorithm to earthquake-excited structures comes from the definition of the performance index, J. Performance index given in classical control is the integral of quadratic functions over time interval ( 0, tf ), and hence the input excitation in that time interval should be known a priori. So instantaneous optimal control algorithms have been established using_ the time-dependent performance index J(t)=ZT(t)QZ(t)+Ur(t)RU(t). Performance index J(t) is minimized at every time instant t for all 0<t<tf. Theoptimal control thus obtained is referred to as the instantaneous optimal control algorithm. Instantaneous optimal control algorithms have been developed by Yang for lineer structures. But, in reality, many tall buildings undergo large deformation or yielding when subjected to strong earthquake ground motion, and hence, exhibit nonlineer or inelastic behaviour. When the deformations of structures enter into the inelastic range, they are in critical stage. It is needed the protective system most at this critical stage. As a result, active control systems must be able to operate in the nonlineer range of motion for tall buildings. When the active and passive systems are used together passive systems, such as rubber base isolators, exhibit large deformation and inelastic behaviour. This will cause nonlineer equations of motions for the entire structural system. So, active control system should be capable of dealing with nonlineer structures. Traditionally, active control has been applied to linear structures. Control theories for nonlinear systems are very limited. To control nonlinear structures, active pulse control has been investigated recently by Masri and Reinhorn. But, control algorithm used is nonoptimal. In 1988, Yang proposed three optimal control algorithms applicable to flexible nonlinear structures, IXincluding inelastic structures, subjected to general dynamic loads, deterministic or stochastic. These optimal control algorithms are simple and reliable for on-line control operations and they are effective in mitigating structural oscillation. Control forces are continuous in time and active control can be implemented by electrohydraulic servomechanisms along with tendons or mass dampers. In formulation, a one-dimensional nonlinear building structure implemented by an active tendon control system is assumed. Structure is idealized by an n-degree-of- freedom system and subjected # to one-dimensional earthquake ground acceleration X0(t). Damping force vector and stiffness restoring vector are nonlinear functions of floor velocity vector and deformation vector. C*ij(t-8t) and K*4j(t-St) are influence coefficients which represent the tangent damping and tangent stiffness at t-5t (Clough,1975). The system of nonlinear equations is solved using Wilson-9 numerical integration procedure. The solution is expressed in state-space form. Wilson constant is chosen as 1.37. For a particular case, damping is assumed to be linear viscous damping. So nonlinearity comes from the stiffness vector. For nonlinear structures, the same time dependent objective function given for linear structures is minimized. Using the minimum principle of Pontryagin, optimal control vector U(t) are calculated for three instantaneous optimal control algorithms. In instantaneous optimal closed-loop control, control vector U(t) is given by the equation U(t)=-R-1A2 QZ(t) It is important that for the instantaneou optimal closed-loop control algorithm, the measurement of earthquake ground acceleration is not necessary. The control vector U(t) is regulated only by the measured state vector Z ( t ). In our program, we used instantaneous optimal control algorithm developed for nonlinear structures. To illustrate the effectiveness of this control algorithm three numerical examples are solved. The structure is assumed to exhibit nonlinear material behaviour with bilinear elastic-plastic characteristics. For simplicity, damping is assumed to be linear viscous damping.It should be mentioned that three instantaneous optimal control algorithms result in identical structure response quantities as well as identical control force under ideal control environment since they minimize the same time dependent objective function. In numerical examples, for illustrative purposes we considered an eight-story building in which every storyunit is identically constructed. The structural properties of each story unit are assumed to be the same. So masses, elastic stiffnesses and post-elastic stiffnesses of stories are equal. Internal damping coefficient of each story is also the same. The external damping is assumed to be zero. An active mass damper is installed on the top floor of the building. With an active mass damper, the structural response depends on the weighting matrices R and Q. In the examples, the weighting matrix R consists of only one element which is chosen as 0.001. Q matrix has the dimension of (18x18). In the first example, we investigated the behaviour of the structure with active mass damper subjected to a simulated earthquake ground acceleration. For demonstrative purposes, the earthquake ground acceleration is modeled as a uniformly modulated nonstationary random process. This nonstationary random process is obtained by multiplying a stationary random process with zero mean with a deterministic nonnegative envelope function. Parameters of envelope function should be selected appropriately to reflect the shape and duration of the earthquake qround acceleration. As a spectral density function for the stationary process, the spectral density function given by Kanai-Tajimi is used. In simulation, fast fourier trasform method is used. Then using the computer program, the maximum response, maximum control force and maximum shear force for each story are calculated. In the second example, instead of simulated earthquake we used N-S component of Erzincan earthquake occured in 1992. In the thirth example as an input excitation we used Elcentro earthquake. We saw that the story displacements and control forces increased for stronger earthquakes. In the first example and second examples, structural response of entire building is well within the elastic limits. But, for the stronger eartquakes only the top floors' responses are within the elastic limits. Control efficiency is regulated at every time instant by the weighting matrices Q and R. xiIn order to guarantee that the structural response be always within the specified limits, weighting matrices should be time-dependent and they should be adaptive to the feedback response at every time instant t. XII
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