基于非概率可靠性的钢坯吊具结构优化研究
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摘要
钢坯吊具是一种量大面广的设备,主要用于转运重物。在钢坯吊具的设计、加工、运行等各个环节,都存在着大量不可测或不可控因素,影响钢坯吊具设计寿命,降低可靠程度。考虑钢坯吊具本身的不确定性,本文将区间有限元与非概率理论相结合,应用于钢坯吊具可靠性研究中,并对钢坯吊具主要元件及其系统进行可靠性分析,将非概率可靠度指标作为约束,引入到优化设计的数学模型中,对其进行可靠性优化设计,为钢坯吊具的不确定性设计提供有力的理论支持。
(1)研究了基于区间分析的结构非概率可靠性问题。将区间分析与结构可靠性联系起来,研究了具有区间特性的设计参数与结构响应之间的映射关系,分析了能够描述结构可靠性的非概率可靠性指标,利用实例分析了区间运算中存在的区间扩张问题。
(2)将区间有限元和非概率可靠性理论相结合,建立了基于区间有限元分析结构非概率可靠性的方法,用于解决钢坯吊具可靠性问题,并定义了区间有限元的敏感性因子来描述不确定参数对结构响应的影响程度。对区间有限元控制方程,提出了利用一阶泰勒展开法和改进的迭代算法对其进行求解,来获得结构响应的变化区间,结合非概率可靠性指标定义,确定结构的可靠程度。
(3)结合区间有限元的非概率可靠性分析方法,对钢坯吊具中连杆、吊梁及钳臂的可靠性进行评估,并分析结构响应对不确定参数的敏感程度。首先分析了连杆的功能函数为隐式情况下,利用支持向量机回归拟合,得到其功能函数,并分析了连杆可靠性及敏感性；然后考虑到吊梁在强度、刚度及稳定性三种失效模式下,对结构的可靠性及敏感性进行分析,并利用全局优化算法对区间有限元控制方程进行求解,得到吊梁的结构响应区间;最后在分析钳臂可靠性及敏感性的基础上,对钳臂处于不同可靠性指标下进行优化求解,获得设计值。
(4)提出了钢坯吊具系统的非概率可靠性分析方法,并基于非概率可靠性指标进行了系统优化。针对钢坯吊具系统处于多种失效模式下,如何确定主要失效模式,提出了利用增量载荷法来寻找主要失效模式,并确定钢坯吊具系统的状态方程,利用非概率可靠性指标的定义,分析了系统可靠性,该方法计算方便、简单,而且.比较适合工程实际中解决系统可靠性问题。
Billet hanging is a special equipment for transporting the heavy, and it's widely. In design, processing, operation and other link of billet hanging, there is this large uncertain or controlled factor that influence design life and reliability of billet hanging. Consider the uncertainty itself, in this paper the interval finite element combining with the probability theory is applied to billet hanging reliability analysis. And main components and system reliability of billet hanging were analyzed. The optimization model merged into the non-probabilistic reliability index as a constraint may be solved by optimization method. That design method provided the strong theoretical support for billet hanging design. Therefore, the main research contents were list as following:
(1) The structure non-probabilistic reliability based on interval analysis. Linked Interval analysis with structural reliability, the mapping relationship between the design parameters with a range of characteristics and structural response can be made known, and the non-probabilistic reliability index was described. By a example of plate-hole hanging lug, we analyzed the interval extension existing in interval arithmetic.
(2) Combining the interval finite element method with non-probabilistic reliability theory, a method for analyzing structure non-probabilistic reliability based on the interval finite element was proposed. The method was used to solve the reliability problems of billet hanging, and a sensitivity factor based on the interval finite element for describing the influence degree of the uncertain parameters to structural response was defined. For solving the interval finite element equations, two methods that were the first order Taylor expansion method and the improved iterative algorithm were put forward. By virtue of them, we can obtain the fluctuation range of structure response, and combining with the definition of the non-probabilistic reliability index, we can estimate the reliability degree.
(3) Combined with the interval finite element non-probabilistic reliability analysis method, assess the reliability of connecting rods, hanging beams and clamp arm of Billet hanging and analyzed the sensitivity of the uncertain parameters to structural response of them. First, when structure state function was implicit, taking connecting rob for example, we can obtain structure state function by use of the ability of support vector machine regression, and analyzed the reliability and sensitivity of it. Then, considering in strength, stiffness and stability failure modes of the hanging beam, we analyzed the structure reliability and sensitivity, and solved the interval finite element equations by global optimization algorithm, and got the range of structural response of hanging beams. Finally, based on the reliability and sensitivity of clamp arm, the best design value of uncertain parameters may be obtained by the optimization in different reliability index.
(4) Putting forward the system non-probabilistic reliability analysis method for billet hanging, and optimizing the system of billet hanging based on the non-probabilistic probability reliability index. When billet hanging system is in a variety of failure mode, how to determine the main failure mode. We may find the main one in a variety of failure mode by the method of incremental load, then the system state equation may be built. According to the definition of non-probabilistic reliability index, the reliability of billet hanging system was analyzed. The results show, this method is convenient and simple, and it is more suitable for solving system reliability problems in practical engineering.
(1)研究了基于区间分析的结构非概率可靠性问题。将区间分析与结构可靠性联系起来,研究了具有区间特性的设计参数与结构响应之间的映射关系,分析了能够描述结构可靠性的非概率可靠性指标,利用实例分析了区间运算中存在的区间扩张问题。
(2)将区间有限元和非概率可靠性理论相结合,建立了基于区间有限元分析结构非概率可靠性的方法,用于解决钢坯吊具可靠性问题,并定义了区间有限元的敏感性因子来描述不确定参数对结构响应的影响程度。对区间有限元控制方程,提出了利用一阶泰勒展开法和改进的迭代算法对其进行求解,来获得结构响应的变化区间,结合非概率可靠性指标定义,确定结构的可靠程度。
(3)结合区间有限元的非概率可靠性分析方法,对钢坯吊具中连杆、吊梁及钳臂的可靠性进行评估,并分析结构响应对不确定参数的敏感程度。首先分析了连杆的功能函数为隐式情况下,利用支持向量机回归拟合,得到其功能函数,并分析了连杆可靠性及敏感性；然后考虑到吊梁在强度、刚度及稳定性三种失效模式下,对结构的可靠性及敏感性进行分析,并利用全局优化算法对区间有限元控制方程进行求解,得到吊梁的结构响应区间;最后在分析钳臂可靠性及敏感性的基础上,对钳臂处于不同可靠性指标下进行优化求解,获得设计值。
(4)提出了钢坯吊具系统的非概率可靠性分析方法,并基于非概率可靠性指标进行了系统优化。针对钢坯吊具系统处于多种失效模式下,如何确定主要失效模式,提出了利用增量载荷法来寻找主要失效模式,并确定钢坯吊具系统的状态方程,利用非概率可靠性指标的定义,分析了系统可靠性,该方法计算方便、简单,而且.比较适合工程实际中解决系统可靠性问题。
Billet hanging is a special equipment for transporting the heavy, and it's widely. In design, processing, operation and other link of billet hanging, there is this large uncertain or controlled factor that influence design life and reliability of billet hanging. Consider the uncertainty itself, in this paper the interval finite element combining with the probability theory is applied to billet hanging reliability analysis. And main components and system reliability of billet hanging were analyzed. The optimization model merged into the non-probabilistic reliability index as a constraint may be solved by optimization method. That design method provided the strong theoretical support for billet hanging design. Therefore, the main research contents were list as following:
(1) The structure non-probabilistic reliability based on interval analysis. Linked Interval analysis with structural reliability, the mapping relationship between the design parameters with a range of characteristics and structural response can be made known, and the non-probabilistic reliability index was described. By a example of plate-hole hanging lug, we analyzed the interval extension existing in interval arithmetic.
(2) Combining the interval finite element method with non-probabilistic reliability theory, a method for analyzing structure non-probabilistic reliability based on the interval finite element was proposed. The method was used to solve the reliability problems of billet hanging, and a sensitivity factor based on the interval finite element for describing the influence degree of the uncertain parameters to structural response was defined. For solving the interval finite element equations, two methods that were the first order Taylor expansion method and the improved iterative algorithm were put forward. By virtue of them, we can obtain the fluctuation range of structure response, and combining with the definition of the non-probabilistic reliability index, we can estimate the reliability degree.
(3) Combined with the interval finite element non-probabilistic reliability analysis method, assess the reliability of connecting rods, hanging beams and clamp arm of Billet hanging and analyzed the sensitivity of the uncertain parameters to structural response of them. First, when structure state function was implicit, taking connecting rob for example, we can obtain structure state function by use of the ability of support vector machine regression, and analyzed the reliability and sensitivity of it. Then, considering in strength, stiffness and stability failure modes of the hanging beam, we analyzed the structure reliability and sensitivity, and solved the interval finite element equations by global optimization algorithm, and got the range of structural response of hanging beams. Finally, based on the reliability and sensitivity of clamp arm, the best design value of uncertain parameters may be obtained by the optimization in different reliability index.
(4) Putting forward the system non-probabilistic reliability analysis method for billet hanging, and optimizing the system of billet hanging based on the non-probabilistic probability reliability index. When billet hanging system is in a variety of failure mode, how to determine the main failure mode. We may find the main one in a variety of failure mode by the method of incremental load, then the system state equation may be built. According to the definition of non-probabilistic reliability index, the reliability of billet hanging system was analyzed. The results show, this method is convenient and simple, and it is more suitable for solving system reliability problems in practical engineering.
引文
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