被动控制器优化设计方法研究
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摘要
中国是一个多震害国家,长期的地震灾害给我国造成了巨大的损失。建筑结构的防灾减震已愈来愈受到人们的重视,结构振动控制技术也随之飞速发展,主动和被动控制技术研究都已成为当前研究热点。其中被动控制不需要外部能源、技术简单、造价低、性能可靠,因此广泛应用于实际结构,被动控制方法的研究显得尤其重要。本文以平面框架结构模型和三维实体结构模型为研究对象,基于能量的观点,从被动控制器参数优化和安装数目及位置优化两个方面出发,对被动控制器控制结构地震响应的优化设计方法进行了研究,并分析了控制结果对安装次结构的楼层反应谱的影响。文中主要内容如下:
(1)建立了平面框架结构体系的动力学模型,研究了三种被动控制器(包括弹性及阻尼元件)的参数优化设计方法,即在时域内基于LQR理论和矩阵初等变换时运用最小二乘法优化方法、在频域内的等效最优控制方法和在频域内以体系的能量指标J为目标函数时的遗传算法优化方法;对于每种参数优化方法,再基于结构在频域内的响应,从能量的角度出发,运用与时域相对应的控制器性能指标ΔJ对被动控制器的数目和安装数目及位置进行优化。优化设计后建立了安装次结构时平面框架结构体系的动力学模型,研究了控制器参数优化设计结果对楼层反应谱的影响。算例表明,以能量指标J为目标函数时的遗传算法参数优化方法得到的控制效果较好;加速度楼层反应谱能够直观可靠的反应结构控制效果。
(2)建立了三维实体结构的动力学模型,在以体系的能量指标J为目标函数时的遗传算法优化方法前提下,讨论了逐个优化和逐层优化阻尼器参数两种方法。逐个优化时,对单个阻尼器单独布置在结构某一榀框架时对阻尼器的参数进行优化,然后建立了安装有次结构时三维实体结构体系的动力学模型,根据各阻尼器对结构顶层安装次结构时的加速度反应谱的控制效果对阻尼器的数目和安装位置进行优化。逐层优化时,对一组阻尼器按楼层同时布置在某层各榀框架时阻尼器的参数进行优化,此时阻尼器的数目和安装位置优化按控制器的性能指标ΔJ为依据进行。算例对比了逐个优化、逐层优化的遗传算法和复形调优法三者的控制效果,验证了两种优化方法的有效性,建议采用遗传算法逐层优化。
Earthquake disaster is one of the most serious disasters, which may result in heavy casualties and economic losses. Therefore, the disasterproof and aseismic design of civil structures are growing recognized by structure engineers and scientific researchers. With the development of vibration control technology in civil engineering, Active Control and Passive Control has become a worldwide hot topic. Since the passive control does not require extra power, the passive control also has many advantages such as simple technique, low cost, dependable performance and so on. Due to its outstanding merits, passive control is widely used in practical buildings. In this thesis, against plane frame structure model and three-dimensional shear-type structure model, the method of Optimal Design method for Passive Control Devices which decrease seismic structural response. The main content of this thesis is as follows:
(1) The mathematical model of the plane frame structure system is established in structural dynamics. Based on this, three method for the optimal design of passive control devices composed of stiffness components and damping components are discussed: 1), Based on the theories of LQR algorithm and elementary transformation of matrix, the least square method is used to optimize the parameters of passive control devices; 2), the optimal parameters can be obtained by using the equivalent optimal control method;3), the optimal parameters can be obtained by using the genetic algorithm method in which the energy index (J) of the plane frame structure is used as the object function. For each method, in frequency domain, based on the dynamic responses of the plane frame structure system, the performance index of control devices AJ is proposed according to the energy concept used in stochastic dynamics, and the optimal number and placement of passive control devices can be obtained according to this performance index. Then the mathematic model and the floor response spectrum are analyzed by considering a secondary structure which is installed on one floor and coupled with the plane frame structure system. As shown in the numerical examples, the third method is the most effective method; control effect of Passive Control Devices can be reflected by the acceleration floor response spectrum.
(2) The mathematical model of a typical three-dimensional shear-type structure is established in structural dynamics, two methods for the optimal design of passive control devices installed in the three-dimensional structure are discussed: 1), the optimization design for the parameters of passive control devices is independently, proceed from one damper after another. The optimal parameters can be obtained by using the genetic algorithm when the energy index (J) of the three-dimensional is used as the object function. Then the mathematic model and the floor response spectrum are analyzed by considering a secondary structure which is installed on one floor and coupled with the three-dimensional structure system, if the control effect of acceleration floor response spectrum of the three-dimensional structure system by one control device is well, this control device is preserved, so the optimal number and placement of passive control devices can be obtained according to this processes. 2), the optimization design for the parameters of passive control device is holisticly proceed from one floor after another. The optimal parameters can also be obtained by using the genetic algorithm in which the energy index of the three-dimensional structure (J) is the object function. The performance index of control devices△J is proposed according to the energy concept used in stochastic dynamics, and the optimal number and placement of passive control devices can be obtained according to this performance index. As shown in the numerical examples, in order to test the effect of the method proposed in this part, the first method, the second method and the complex optimization method are compared. According to the control result, the second method is suggested.
(1)建立了平面框架结构体系的动力学模型,研究了三种被动控制器(包括弹性及阻尼元件)的参数优化设计方法,即在时域内基于LQR理论和矩阵初等变换时运用最小二乘法优化方法、在频域内的等效最优控制方法和在频域内以体系的能量指标J为目标函数时的遗传算法优化方法;对于每种参数优化方法,再基于结构在频域内的响应,从能量的角度出发,运用与时域相对应的控制器性能指标ΔJ对被动控制器的数目和安装数目及位置进行优化。优化设计后建立了安装次结构时平面框架结构体系的动力学模型,研究了控制器参数优化设计结果对楼层反应谱的影响。算例表明,以能量指标J为目标函数时的遗传算法参数优化方法得到的控制效果较好;加速度楼层反应谱能够直观可靠的反应结构控制效果。
(2)建立了三维实体结构的动力学模型,在以体系的能量指标J为目标函数时的遗传算法优化方法前提下,讨论了逐个优化和逐层优化阻尼器参数两种方法。逐个优化时,对单个阻尼器单独布置在结构某一榀框架时对阻尼器的参数进行优化,然后建立了安装有次结构时三维实体结构体系的动力学模型,根据各阻尼器对结构顶层安装次结构时的加速度反应谱的控制效果对阻尼器的数目和安装位置进行优化。逐层优化时,对一组阻尼器按楼层同时布置在某层各榀框架时阻尼器的参数进行优化,此时阻尼器的数目和安装位置优化按控制器的性能指标ΔJ为依据进行。算例对比了逐个优化、逐层优化的遗传算法和复形调优法三者的控制效果,验证了两种优化方法的有效性,建议采用遗传算法逐层优化。
Earthquake disaster is one of the most serious disasters, which may result in heavy casualties and economic losses. Therefore, the disasterproof and aseismic design of civil structures are growing recognized by structure engineers and scientific researchers. With the development of vibration control technology in civil engineering, Active Control and Passive Control has become a worldwide hot topic. Since the passive control does not require extra power, the passive control also has many advantages such as simple technique, low cost, dependable performance and so on. Due to its outstanding merits, passive control is widely used in practical buildings. In this thesis, against plane frame structure model and three-dimensional shear-type structure model, the method of Optimal Design method for Passive Control Devices which decrease seismic structural response. The main content of this thesis is as follows:
(1) The mathematical model of the plane frame structure system is established in structural dynamics. Based on this, three method for the optimal design of passive control devices composed of stiffness components and damping components are discussed: 1), Based on the theories of LQR algorithm and elementary transformation of matrix, the least square method is used to optimize the parameters of passive control devices; 2), the optimal parameters can be obtained by using the equivalent optimal control method;3), the optimal parameters can be obtained by using the genetic algorithm method in which the energy index (J) of the plane frame structure is used as the object function. For each method, in frequency domain, based on the dynamic responses of the plane frame structure system, the performance index of control devices AJ is proposed according to the energy concept used in stochastic dynamics, and the optimal number and placement of passive control devices can be obtained according to this performance index. Then the mathematic model and the floor response spectrum are analyzed by considering a secondary structure which is installed on one floor and coupled with the plane frame structure system. As shown in the numerical examples, the third method is the most effective method; control effect of Passive Control Devices can be reflected by the acceleration floor response spectrum.
(2) The mathematical model of a typical three-dimensional shear-type structure is established in structural dynamics, two methods for the optimal design of passive control devices installed in the three-dimensional structure are discussed: 1), the optimization design for the parameters of passive control devices is independently, proceed from one damper after another. The optimal parameters can be obtained by using the genetic algorithm when the energy index (J) of the three-dimensional is used as the object function. Then the mathematic model and the floor response spectrum are analyzed by considering a secondary structure which is installed on one floor and coupled with the three-dimensional structure system, if the control effect of acceleration floor response spectrum of the three-dimensional structure system by one control device is well, this control device is preserved, so the optimal number and placement of passive control devices can be obtained according to this processes. 2), the optimization design for the parameters of passive control device is holisticly proceed from one floor after another. The optimal parameters can also be obtained by using the genetic algorithm in which the energy index of the three-dimensional structure (J) is the object function. The performance index of control devices△J is proposed according to the energy concept used in stochastic dynamics, and the optimal number and placement of passive control devices can be obtained according to this performance index. As shown in the numerical examples, in order to test the effect of the method proposed in this part, the first method, the second method and the complex optimization method are compared. According to the control result, the second method is suggested.
引文
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