基于实验数据挖掘与细胞自动机的结构分析方法
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摘要
传统的结构分析技术,以有限单元法为代表,都是基于本构关系和机理的结构工作性能的研究,并应用于所有工程领域。然而,结构本身变异性导致的结构反应与理论分析结果的差别,是长期存在但又没有深入研究的问题。目前,对于变异性的研究,一般处理为随机的变异系数,再与结构的某些物理参数相结合。这样处理变异性的方法,虽然能反映结构的变异性,但是存在局限性和片面性,缘于这种方法只是经验与统计参数分析,并未给出基于理论与实验的结构变异性模型,自然在诸如砌体结构的一些有限元分析中,很难得到与试验结果接近的预测结果。
本文通过对砌体结构实验与理论分析的结果观察研究发现:结构变异性不是完全随机的因素,过去按随机因素处理的变异性中存在确定性,而且这种确定性与结构构造(几何,约束)有关。因此,就激发了这样的想法:应用最新的分析理论,例如数据挖掘与细胞自动机等智能技术,对这种确定性进行提炼建模,然后反馈到现有分析技术中,改进分析方法,提高预测精度,达到更精确地预测结构反应的目的。
首先,对大量不同几何尺寸,不同边界约束条件和不同受力方式的砌体墙板进行理论数值与试验结果的对比分析,重点考察了对比数值的趋势性与分布,从中显现了一个规律性,即在同一墙板或者任意几何与约束性质不同的墙板内的各个区域,如果结构内两个局部区域的相对位置类似、以及控制两个区域的约束类型类似,则相应的理论与试验数比值或者比值的局部分布模式就“相同”。据此,本文提出了结构局域性质的概念,以描述结构区域在相对位置与约束性质上的类似。这样,就有了结构局域性质数据挖掘的雏形,从而又提出了对于其它结构体系进行数据挖掘,获得局域性质系数的方法。
进而,本文提出,将有限元分析计算的位移值与试验实测位移值的比值定义为局域性质系数。局域性质系数的意义体现在类似结构局部区域的性质类似,就是说,不同结构上的两个类似区域具有近似或相同的局域性质系数。因此,可以应用局域性质系数修正砌体墙板的有限元模型,具体做法:先将全局弹性模量与各个区域的局域性质系数相乘,使结构不同区域的弹性模量不同;再进行结构的有限元分析。通过三组试验墙板(竖向荷载作用墙板、横向荷载作用小墙、横向荷载作用墙板)的计算表明:应用局域性质系数进行结构的有限元分析,得到的分析结果更接近于试验结果,尤其是在墙板中间区域,有限元的结果与试验结果吻合更好。
这样,通过简单数据挖掘得到了试验结构的各个局域性质系数,该方法能将结构一部分本是确定的“变异量”从原来的“随机量”中提取出来,使这部分确定性的结构性质定量地体现在结构分析中,使分析结果更真实地反映实际情况。
接着,本文探讨了类似区域的性质以及匹配准则。由于在表现区域状态以及自动匹配类似区域上的困难,本文借用了ZHOU最早在砌体墙板分析中建立的细胞自动机应用技术,并将其拓展到其它结构体系,给出了相应的状态值的算法。也就是说,本文给出了一种计算各种结构局部区域状态值的统一公式,并通过聚类分析建立了类似区域的匹配准则。同时,为甄别类似区域匹配准则的适用范围,定义了结构相似度的概念,给出了结构相似度的计算公式,量化了匹配结果准确性的判断。
最后,以算例验证上面提出的新概念新方法。除应用前三组试验墙板提炼的局域性质系数修正各自的有限元模型进行分析外,重新选择第四组试验墙板SB06作为基础板,预测横向荷载作用墙板的不同变形行为。由于基础板和待预测板的几何尺寸不一致,应用细胞自动机模型时,对传递函数初值和传递系数进行修正,提出长度和高度两个方向的修正系数公式。在基础板边界初始值和传递系数不变的情况下,通过修正系数调整待预测板的边界初始值和传递系数,从而匹配出两者间的类似区域,进而预测出其变形。
应用智能技术进行结构分析,挖掘局域性质系数,匹配类似区域,修正有限元模型,这种方法不仅能预测出一种变形行为,还能通过调整传递系数实现多种变形行为的预测。
The traditional structural analysis techniques, such as the finite element method, study structural performances all based on the constitutive condition and mechanism, which are applied to all areas of engineering. However, an issue has existed for a long time, that is, the difference between the structural response caused by the variability of the structure itself and the corresponding analytical result has not been studied fully in theory. At present, the variability of a structure is generally treated as a random factor and then connected with some physical parameters of the structure. This method on dealing with variability can only reflect the variability of structure limitedly and one-sidedly. In other words, this treatment does not present the structural variability in basis of theory and mechanism and is only based on the experience with statistical parametric analysis. Hence, it is difficult for the FEA to predict the structural response of the masonry structure close to experimental ones.
During experimental and theoretical analysis of masonry structure, it was found that structural variability is not completely caused by random factors, but it exists in certainty, which is affected by the structural geometrical property and boundary constraints or others. Therefore, an idea was inspired in this study: If it is possible that the latest intelligent techniques, such as data mining and cellular automata, are applied to model this certainty existed in variability, and then the model is back fed to the existing analytical methods, it can improve the analytical methods so that the predicted structural response is more accurate.
First, a comparative analysis of their theoretical and experimental results is done to study the tendency and distribution of the comparative values for a large number of masonry wall panels inclusive of different configurations. From the study, a regularity emerges: for the various zones within the same wall panel or different wall panels with different configurations, if the relative positions of two local zones are similar, and the constraints governing the two zones are also similar, the ratio between theoretical and experimental values are basically the same; besides, the distribution patterns of the ratio values at local regions are also similar. Accordingly, this paper presents the concept of the structural local property, which describes the similarity of the relative positions of the zones and the structural constraints. In this way, a prototype of the structural local property is formed corresponding to data mining. Furthermore, the method is proposed to obtain the local property coefficient of other structural systems based on the data mining technology.
Second, this paper defines the local property coefficient as the ratio of the displacement values of the finite element analysis to the corresponding experimental displacement values at measured points. The significance of coefficient is in the similar property relating to the similar local zones within structures, that is, two similar zones in different structures have the same local property coefficient. Therefore, the finite element model of masonry wall panel can be modified by the local property coefficients of all local zones. The way for the modification is: the global elastic modulus is multiplied by the local property coefficients of all zones, so that the elastic modulus of the structure in different zones is different; then, the modified elastic modulus is used in the FEA of the structure. By three sets of test wallets and wall panels, the vertically loaded wall panel, the laterally loaded wallette and the test of laterally loaded wall panel, the application of the local property coefficients in their FEA can make the analytical results closer to the experimental results, especially in the center zones of the wall panel。
In this way, it obtains the various local property coefficients about test structures, through a simple data mining. This method can extract a part of“variance”of the structure which is considered random in the past analytical tasks; and this part of certainty of the structural“variance”property can reflect in the quantitative analysis of the structure and makes the analysis results more accurately embody the real situation.
Third, the paper studies the property of the similar zone and the corresponding rule for matching zone similarity. As it is difficult to describe the regional states and to automatically match similar zones, this paper extends Zhou’s research results, the cellular automata model of masonry wall panel, to other structural systems and gives out the new algorithm of the zone state value. In other words, this paper presents a general formula for calculating the zone state value of various structures, and establishes the rule for matching similar zone by clustering analysis. Meanwhile, in order to discriminate the scope of rule for matching zone similarity, the concept of structural similarity level is proposed and the corresponding formula is given to compute the similarity level. Structural similarity level quantifies the accuracy of the matching results.
Finally, it verifies the above new concept and new method by case study. Three sets of local property coefficients are applied to modify the corresponding finite element models. Besides, taking the fourth set of the test panel named Panel SB06 as the base panel, the FEA of the wall panel is done to predict the different deformation modes of other unknown panels. As the geometrical size of predicted panel different from that of the base panel, it is necessary to amend the initial values of the transfer function and transfer coefficients, in application of cellular automata model. This paper presents two formulas for modifying initial value in the directions of length and height. In the case of the constant boundary initial value and the transfer coefficient of the base panel, both values of the predicted panel are amended using the two formulas and then the similar zones between the two panels are matched using the proposed rule; thus, the deformation of unknown panel can be predicted accurately.
The method that intelligent techniques are used to conduct data mining of local property of structures, to match zone similarity and improve the FEA model, can predict not only a deformation mode, but also a set of deformation modes by adjusting the values of the transition efficient.
本文通过对砌体结构实验与理论分析的结果观察研究发现:结构变异性不是完全随机的因素,过去按随机因素处理的变异性中存在确定性,而且这种确定性与结构构造(几何,约束)有关。因此,就激发了这样的想法:应用最新的分析理论,例如数据挖掘与细胞自动机等智能技术,对这种确定性进行提炼建模,然后反馈到现有分析技术中,改进分析方法,提高预测精度,达到更精确地预测结构反应的目的。
首先,对大量不同几何尺寸,不同边界约束条件和不同受力方式的砌体墙板进行理论数值与试验结果的对比分析,重点考察了对比数值的趋势性与分布,从中显现了一个规律性,即在同一墙板或者任意几何与约束性质不同的墙板内的各个区域,如果结构内两个局部区域的相对位置类似、以及控制两个区域的约束类型类似,则相应的理论与试验数比值或者比值的局部分布模式就“相同”。据此,本文提出了结构局域性质的概念,以描述结构区域在相对位置与约束性质上的类似。这样,就有了结构局域性质数据挖掘的雏形,从而又提出了对于其它结构体系进行数据挖掘,获得局域性质系数的方法。
进而,本文提出,将有限元分析计算的位移值与试验实测位移值的比值定义为局域性质系数。局域性质系数的意义体现在类似结构局部区域的性质类似,就是说,不同结构上的两个类似区域具有近似或相同的局域性质系数。因此,可以应用局域性质系数修正砌体墙板的有限元模型,具体做法:先将全局弹性模量与各个区域的局域性质系数相乘,使结构不同区域的弹性模量不同;再进行结构的有限元分析。通过三组试验墙板(竖向荷载作用墙板、横向荷载作用小墙、横向荷载作用墙板)的计算表明:应用局域性质系数进行结构的有限元分析,得到的分析结果更接近于试验结果,尤其是在墙板中间区域,有限元的结果与试验结果吻合更好。
这样,通过简单数据挖掘得到了试验结构的各个局域性质系数,该方法能将结构一部分本是确定的“变异量”从原来的“随机量”中提取出来,使这部分确定性的结构性质定量地体现在结构分析中,使分析结果更真实地反映实际情况。
接着,本文探讨了类似区域的性质以及匹配准则。由于在表现区域状态以及自动匹配类似区域上的困难,本文借用了ZHOU最早在砌体墙板分析中建立的细胞自动机应用技术,并将其拓展到其它结构体系,给出了相应的状态值的算法。也就是说,本文给出了一种计算各种结构局部区域状态值的统一公式,并通过聚类分析建立了类似区域的匹配准则。同时,为甄别类似区域匹配准则的适用范围,定义了结构相似度的概念,给出了结构相似度的计算公式,量化了匹配结果准确性的判断。
最后,以算例验证上面提出的新概念新方法。除应用前三组试验墙板提炼的局域性质系数修正各自的有限元模型进行分析外,重新选择第四组试验墙板SB06作为基础板,预测横向荷载作用墙板的不同变形行为。由于基础板和待预测板的几何尺寸不一致,应用细胞自动机模型时,对传递函数初值和传递系数进行修正,提出长度和高度两个方向的修正系数公式。在基础板边界初始值和传递系数不变的情况下,通过修正系数调整待预测板的边界初始值和传递系数,从而匹配出两者间的类似区域,进而预测出其变形。
应用智能技术进行结构分析,挖掘局域性质系数,匹配类似区域,修正有限元模型,这种方法不仅能预测出一种变形行为,还能通过调整传递系数实现多种变形行为的预测。
The traditional structural analysis techniques, such as the finite element method, study structural performances all based on the constitutive condition and mechanism, which are applied to all areas of engineering. However, an issue has existed for a long time, that is, the difference between the structural response caused by the variability of the structure itself and the corresponding analytical result has not been studied fully in theory. At present, the variability of a structure is generally treated as a random factor and then connected with some physical parameters of the structure. This method on dealing with variability can only reflect the variability of structure limitedly and one-sidedly. In other words, this treatment does not present the structural variability in basis of theory and mechanism and is only based on the experience with statistical parametric analysis. Hence, it is difficult for the FEA to predict the structural response of the masonry structure close to experimental ones.
During experimental and theoretical analysis of masonry structure, it was found that structural variability is not completely caused by random factors, but it exists in certainty, which is affected by the structural geometrical property and boundary constraints or others. Therefore, an idea was inspired in this study: If it is possible that the latest intelligent techniques, such as data mining and cellular automata, are applied to model this certainty existed in variability, and then the model is back fed to the existing analytical methods, it can improve the analytical methods so that the predicted structural response is more accurate.
First, a comparative analysis of their theoretical and experimental results is done to study the tendency and distribution of the comparative values for a large number of masonry wall panels inclusive of different configurations. From the study, a regularity emerges: for the various zones within the same wall panel or different wall panels with different configurations, if the relative positions of two local zones are similar, and the constraints governing the two zones are also similar, the ratio between theoretical and experimental values are basically the same; besides, the distribution patterns of the ratio values at local regions are also similar. Accordingly, this paper presents the concept of the structural local property, which describes the similarity of the relative positions of the zones and the structural constraints. In this way, a prototype of the structural local property is formed corresponding to data mining. Furthermore, the method is proposed to obtain the local property coefficient of other structural systems based on the data mining technology.
Second, this paper defines the local property coefficient as the ratio of the displacement values of the finite element analysis to the corresponding experimental displacement values at measured points. The significance of coefficient is in the similar property relating to the similar local zones within structures, that is, two similar zones in different structures have the same local property coefficient. Therefore, the finite element model of masonry wall panel can be modified by the local property coefficients of all local zones. The way for the modification is: the global elastic modulus is multiplied by the local property coefficients of all zones, so that the elastic modulus of the structure in different zones is different; then, the modified elastic modulus is used in the FEA of the structure. By three sets of test wallets and wall panels, the vertically loaded wall panel, the laterally loaded wallette and the test of laterally loaded wall panel, the application of the local property coefficients in their FEA can make the analytical results closer to the experimental results, especially in the center zones of the wall panel。
In this way, it obtains the various local property coefficients about test structures, through a simple data mining. This method can extract a part of“variance”of the structure which is considered random in the past analytical tasks; and this part of certainty of the structural“variance”property can reflect in the quantitative analysis of the structure and makes the analysis results more accurately embody the real situation.
Third, the paper studies the property of the similar zone and the corresponding rule for matching zone similarity. As it is difficult to describe the regional states and to automatically match similar zones, this paper extends Zhou’s research results, the cellular automata model of masonry wall panel, to other structural systems and gives out the new algorithm of the zone state value. In other words, this paper presents a general formula for calculating the zone state value of various structures, and establishes the rule for matching similar zone by clustering analysis. Meanwhile, in order to discriminate the scope of rule for matching zone similarity, the concept of structural similarity level is proposed and the corresponding formula is given to compute the similarity level. Structural similarity level quantifies the accuracy of the matching results.
Finally, it verifies the above new concept and new method by case study. Three sets of local property coefficients are applied to modify the corresponding finite element models. Besides, taking the fourth set of the test panel named Panel SB06 as the base panel, the FEA of the wall panel is done to predict the different deformation modes of other unknown panels. As the geometrical size of predicted panel different from that of the base panel, it is necessary to amend the initial values of the transfer function and transfer coefficients, in application of cellular automata model. This paper presents two formulas for modifying initial value in the directions of length and height. In the case of the constant boundary initial value and the transfer coefficient of the base panel, both values of the predicted panel are amended using the two formulas and then the similar zones between the two panels are matched using the proposed rule; thus, the deformation of unknown panel can be predicted accurately.
The method that intelligent techniques are used to conduct data mining of local property of structures, to match zone similarity and improve the FEA model, can predict not only a deformation mode, but also a set of deformation modes by adjusting the values of the transition efficient.
引文
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