CN116522797A - A Method of Predicting the Failure Mode of RC Rectangular Columns Based on Artificial Neural Network - Google Patents
A Method of Predicting the Failure Mode of RC Rectangular Columns Based on Artificial Neural Network Download PDFInfo
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Abstract
Description
技术领域technical field
本发明涉及人工神经网络领域,具体涉及一种基于人工神经网络预测RC矩形柱破坏模式的方法。The invention relates to the field of artificial neural networks, in particular to a method for predicting the failure mode of RC rectangular columns based on artificial neural networks.
背景技术Background technique
根据地震震后的调查和大量的钢筋混凝土柱抗震试验,可以发现不同的配筋特征、截面几何特征、受力情况会导致柱构件不同的破坏模式。一般工程将破坏模式划分为弯曲破坏、弯曲-剪切破坏和剪切破坏。钢筋混凝土矩形柱构件柱的破坏模式对其延性、抗震性能有着直接的影响,故对钢筋混凝土矩形柱构件柱的破坏模式进行预测是至关重要的。According to post-earthquake surveys and a large number of seismic tests of reinforced concrete columns, it can be found that different reinforcement characteristics, section geometric characteristics, and stress conditions will lead to different failure modes of column members. General engineering divides the failure modes into bending failure, bending-shear failure and shear failure. The failure mode of reinforced concrete rectangular column members has a direct impact on its ductility and seismic performance, so it is very important to predict the failure mode of reinforced concrete rectangular column members.
目前常见的,对钢筋混凝土柱构件破坏模式进行预测的方法主要包括:基于剪跨比的预测方法、基于判别分析的预测方法、基于工程简化判别分析的预测方法。其中,基于剪跨比的预测方法只考虑了剪跨比这一个参数;基于工程简化判别分析的预测方法考虑了剪跨比和弯剪比这两个参数;而基于判别分析的预测方法考虑了箍筋间距与截面有效高度比、剪跨比和弯剪比这三个参数。常见的对钢筋混凝土柱构件破坏模式进行预测的方法中均没有考虑配箍率、轴压比、纵向配筋率的影响,其会影响对钢筋混凝土柱构件破坏模式的预测结果的准确性,故钢筋混凝土柱构件破坏模式的预测结果的准确性较低。At present, the methods for predicting the failure mode of reinforced concrete column members mainly include: prediction methods based on shear-span ratio, prediction methods based on discriminant analysis, and prediction methods based on engineering simplified discriminant analysis. Among them, the prediction method based on shear-span ratio only considers the parameter of shear-span ratio; the prediction method based on engineering simplified discriminant analysis considers the two parameters of shear-span ratio and bending-shear ratio; and the prediction method based on discriminant analysis takes into account The three parameters of stirrup spacing and section effective height ratio, shear-span ratio and bending-shear ratio. The common methods for predicting the failure mode of reinforced concrete column members do not consider the influence of hoop ratio, axial compression ratio, and longitudinal reinforcement ratio, which will affect the accuracy of the prediction results of the failure mode of reinforced concrete column members, so The accuracy of prediction results of failure modes of reinforced concrete column members is low.
发明内容Contents of the invention
为了解决现有方法中对钢筋混凝土柱构件破坏模式的预测结果的准确性较低的问题,本发明的目的在于提供一种基于人工神经网络预测RC矩形柱破坏模式的方法,所采用的技术方案具体如下:In order to solve the problem of low accuracy of the prediction results of the failure mode of reinforced concrete column members in the existing methods, the purpose of the present invention is to provide a method for predicting the failure mode of RC rectangular columns based on artificial neural network, and the adopted technical scheme details as follows:
本发明提供了一种基于人工神经网络预测RC矩形柱破坏模式的方法,该方法包括以下步骤:The present invention provides a kind of method based on artificial neural network prediction RC rectangular column damage pattern, and this method comprises the following steps:
基于人工神经网络的预测方法,结合Levenberg Marquardt反向传播训练算法来判别矩形柱构件破坏模式;The prediction method based on the artificial neural network, combined with the Levenberg Marquardt backpropagation training algorithm to identify the failure mode of the rectangular column members;
其中,判别矩形柱构件破坏模式的方法为:设置钢筋混凝土矩形柱构件破坏模式的人工神经网络结构;对矩形柱构件的数据集进行处理,对影响矩形柱构件破坏模式中的配箍率、纵向配筋率、箍筋间距与截面有效高度比、剪跨比、轴压比、弯剪比进行敏感性分析,得到矩形柱构件破坏模式预测结果;对矩形柱构件破坏模式预测结果进行统计性分析。Among them, the method of judging the failure mode of rectangular column members is as follows: setting the artificial neural network structure of the failure mode of reinforced concrete rectangular column members; Sensitivity analysis of reinforcement ratio, ratio of stirrup spacing to section effective height, shear-span ratio, axial compression ratio, and bending-shear ratio to obtain the prediction results of failure mode of rectangular column members; statistical analysis of the prediction results of failure mode of rectangular column members .
优选的,钢筋混凝土矩形柱构件破坏模式的人工神经网络结构的参数包括:输入层节点数、隐藏层节点数、输出层节点数、输入层激活函数,隐藏层激活函数和输出层激活函数。Preferably, the parameters of the artificial neural network structure of the failure mode of the reinforced concrete rectangular column member include: the number of input layer nodes, the number of hidden layer nodes, the number of output layer nodes, the activation function of the input layer, the activation function of the hidden layer and the activation function of the output layer.
优选的,输入层有6个节点,6个节点分别代表配箍率、纵向配筋率、箍筋间距与截面有效高度比、剪跨比、轴压比、弯剪比。Preferably, the input layer has 6 nodes, and the 6 nodes respectively represent the stirrup ratio, the longitudinal reinforcement ratio, the ratio of the stirrup spacing to the effective height of the section, the shear-span ratio, the axial compression ratio, and the bending-shear ratio.
优选的,输入层激活函数的表达式为:Preferably, the expression of the input layer activation function is:
y=f(Wp+b)y=f(Wp+b)
其中,y为激活函数的输出向量;W为权重矩阵;p为初始输入向量;b为偏置向量。Among them, y is the output vector of the activation function; W is the weight matrix; p is the initial input vector; b is the bias vector.
优选的,隐藏层包括两层,第一层有100个节点,第二层有10个节点;其中,隐藏层激活函数为sigmoid函数。Preferably, the hidden layer includes two layers, the first layer has 100 nodes, and the second layer has 10 nodes; wherein, the activation function of the hidden layer is a sigmoid function.
优选的,输出层节点数为3,其中每个节点对应一种破坏模式;其中输出层激活函数为softmax函数。Preferably, the number of nodes in the output layer is 3, and each node corresponds to a damage mode; the activation function of the output layer is a softmax function.
优选的,Levenberg Marquardt反向传播训练算法的表达式为:Preferably, the expression of the Levenberg Marquardt backpropagation training algorithm is:
△x=-[JTJ+μI]-1JTε△x=-[J T J+μI] -1 J T ε
其中,J为雅克比矩阵;JT为雅克比矩阵J的转置矩阵;μ为正常数;I为单位矩阵;ε为网络误差。Among them, J is the Jacobian matrix; J T is the transpose matrix of the Jacobian matrix J; μ is a normal number; I is the identity matrix; ε is the network error.
优选的,弯剪比、剪跨比与钢筋混凝土矩形柱构件破坏模式相关。Preferably, the bending-shear ratio and the shear-span ratio are related to the failure mode of the reinforced concrete rectangular column member.
优选的,使得训练好的人工神经网络的训练数据的准确率达到100%、测试数据的准确率达到95.3%,其中训练数据的最小均方误差为0.0018,测试数据的最小均方误差为0.038。Preferably, the accuracy rate of the training data of the trained artificial neural network reaches 100%, and the accuracy rate of the test data reaches 95.3%, wherein the minimum mean square error of the training data is 0.0018, and the minimum mean square error of the test data is 0.038.
本发明具有如下有益效果:本发明与传统预测方法相比,本发明基于人工神经网络的方法在判别柱构件破坏模式方面比传统的判别预测方法表现得更好。随着柱构件数据集的不断增加,未来人工神经网络模型的准确性会显著提高。伴随着土木工程和人工神经网络的融合发展的同时,可以预见,不仅仅破坏模式预测将使用人工神经网络,甚至构件的变形限值、混凝土材料的本构也可以直接基于人工神经网络(Artificial NeuralNetwork,ANN)结合大量试验数据集得到,原始的试验数据随着人工神经网络的兴起将焕发新的活力。The invention has the following beneficial effects: compared with the traditional prediction method, the method based on the artificial neural network of the invention performs better than the traditional discrimination prediction method in the aspect of discriminating the damage mode of the column member. With the continuous increase of column component data sets, the accuracy of artificial neural network models will be significantly improved in the future. Along with the integration and development of civil engineering and artificial neural network, it is foreseeable that not only the failure mode prediction will use artificial neural network, but even the deformation limit of components and the constitutive of concrete materials can also be directly based on artificial neural network (Artificial Neural Network). , ANN) combined with a large number of experimental data sets, the original experimental data will be rejuvenated with the rise of artificial neural networks.
附图说明Description of drawings
为了更清楚地说明本发明实施例或现有技术中的技术方案和优点,下面将对实施例或现有技术描述中所需要使用的附图作简单的介绍,显而易见地,下面描述中的附图仅仅是本发明的一些实施例,对于本领域普通技术人员来讲,在不付出创造性劳动的前提下,还可以根据这些附图获得其它附图。In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or in the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description The drawings are only some embodiments of the present invention, and those skilled in the art can also obtain other drawings based on these drawings without creative work.
图1为本发明一个实施例所提供的ANN结构示意图;FIG. 1 is a schematic diagram of the ANN structure provided by an embodiment of the present invention;
图2为本发明一个实施例所提供的配箍率对破坏模式影响的箱线图;Fig. 2 is a box-line diagram of the influence of the hoop ratio on the failure mode provided by an embodiment of the present invention;
图3为本发明一个实施例所提供的纵向配筋率对破坏模式影响的箱线图;Fig. 3 is the box diagram of the effect of the longitudinal reinforcement ratio on the failure mode provided by one embodiment of the present invention;
图4为本发明一个实施例所提供的箍筋间距与截面有效高度比对破坏模式影响的箱线图;Fig. 4 is the box diagram of the effect of the ratio of the stirrup spacing and the section effective height on the failure mode provided by an embodiment of the present invention;
图5为本发明一个实施例所提供的剪跨比对破坏模式影响的箱线图;Fig. 5 is the box plot of the influence of shear-span ratio on failure mode provided by one embodiment of the present invention;
图6为本发明一个实施例所提供的轴压比对破坏模式影响的箱线图;Fig. 6 is a box plot of the influence of the axial pressure ratio on the failure mode provided by an embodiment of the present invention;
图7为本发明一个实施例所提供的弯剪比对破坏模式影响的箱线图;Fig. 7 is the box diagram of the influence of the bending-shear ratio on the failure mode provided by one embodiment of the present invention;
图8为本发明一个实施例所提供的Pearson相关系数矩阵;Fig. 8 is the Pearson correlation coefficient matrix provided by one embodiment of the present invention;
图9为本发明一个实施例所提供的数据预测准确率的示意图;Fig. 9 is a schematic diagram of data prediction accuracy provided by an embodiment of the present invention;
图10为本发明一个实施例所提供的最小均方误差的示意图;FIG. 10 is a schematic diagram of the minimum mean square error provided by an embodiment of the present invention;
图11为本发明一个实施例所提供的混淆矩阵的示意图;FIG. 11 is a schematic diagram of a confusion matrix provided by an embodiment of the present invention;
图12为本发明一个实施例所提供的基于弯剪比和剪跨比的破坏模式预测的示意图;Fig. 12 is a schematic diagram of failure mode prediction based on bending-shear ratio and shear-span ratio provided by an embodiment of the present invention;
图13为本发明一个实施例所提供的一种基于人工神经网络预测RC矩形柱破坏模式的方法的示意图。Fig. 13 is a schematic diagram of a method for predicting the failure mode of an RC rectangular column based on an artificial neural network provided by an embodiment of the present invention.
具体实施方式Detailed ways
为了更进一步阐述本发明为达成预定发明目的所采取的技术手段及功效,以下结合附图及较佳实施例,对依据本发明提出的一种基于人工神经网络预测RC矩形柱破坏模式的方法进行详细说明如下。In order to further explain the technical means and effects of the present invention to achieve the intended purpose of the invention, the method for predicting the damage mode of RC rectangular columns based on artificial neural network proposed in the present invention will be carried out below in conjunction with the accompanying drawings and preferred embodiments. The details are as follows.
除非另有定义,本文所使用的所有的技术和科学术语与属于本发明的技术领域的技术人员通常理解的含义相同。Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the technical field of the invention.
本发明实施例提供了一种基于人工神经网络预测RC矩形柱破坏模式的方法的具体实施方法,该方法适用于钢筋混凝土矩形柱构件破坏模式预测的场景。为了解决现有方法中对钢筋混凝土柱构件破坏模式的预测结果的准确性较低的问题。本发明通过基于人工神经网络的预测方法,结合Levenberg Marquardt反向传播训练算法来判别矩形柱构件破坏模式。The embodiment of the present invention provides a specific implementation method of a method for predicting the failure mode of an RC rectangular column based on an artificial neural network, and the method is applicable to a scenario of predicting a failure mode of a reinforced concrete rectangular column member. In order to solve the problem of low accuracy of the prediction results of the failure mode of reinforced concrete column members in the existing methods. The invention uses a prediction method based on an artificial neural network and combines a Levenberg Marquardt backpropagation training algorithm to discriminate the failure mode of a rectangular column member.
下面结合附图具体的说明本发明所提供的一种基于人工神经网络预测RC矩形柱破坏模式的方法的具体方案。A specific scheme of a method for predicting the failure mode of an RC rectangular column based on an artificial neural network provided by the present invention will be described below in conjunction with the accompanying drawings.
请参阅图13,其示出了本实施例的一种基于人工神经网络预测RC矩形柱破坏模式的方法包括以下内容:Please refer to Fig. 13, which shows that a method for predicting the damage mode of RC rectangular columns based on artificial neural network in this embodiment includes the following contents:
基于人工神经网络的预测方法,结合Levenberg Marquardt反向传播训练算法来判别矩形柱构件破坏模式。需要说明的是,Levenberg Marquardt反向传播训练算法即为麦夸特法,为本领域技术人员的公知技术,在此不再进行赘述。The prediction method based on artificial neural network is combined with the Levenberg Marquardt backpropagation training algorithm to identify the failure mode of rectangular column members. It should be noted that the Levenberg Marquardt backpropagation training algorithm is the Marquardt method, which is a well-known technology for those skilled in the art, and will not be repeated here.
其中,判别矩形柱构件破坏模式的方法为:设置钢筋混凝土矩形柱构件破坏模式的人工神经网络结构;对矩形柱构件的数据集进行处理,对影响矩形柱构件破坏模式中的配箍率、纵向配筋率、箍筋间距与截面有效高度比、剪跨比、轴压比、弯剪比进行敏感性分析,得到矩形柱构件破坏模式预测结果;对矩形柱构件破坏模式预测结果进行统计性分析。Among them, the method of judging the failure mode of rectangular column members is as follows: setting the artificial neural network structure of the failure mode of reinforced concrete rectangular column members; Sensitivity analysis of reinforcement ratio, ratio of stirrup spacing to section effective height, shear-span ratio, axial compression ratio, and bending-shear ratio to obtain the prediction results of failure mode of rectangular column members; statistical analysis of the prediction results of failure mode of rectangular column members .
钢筋混凝土矩形柱构件破坏模式的人工神经网络结构的参数包括:输入层节点数、隐藏层节点数、输出层节点数、输入层激活函数,隐藏层激活函数和输出层激活函数;The parameters of the artificial neural network structure of the failure mode of reinforced concrete rectangular column members include: the number of input layer nodes, the number of hidden layer nodes, the number of output layer nodes, the activation function of the input layer, the activation function of the hidden layer and the activation function of the output layer;
其中,输入层有6个节点,6个节点分别代表配箍率、纵向配筋率、箍筋间距与截面有效高度比、剪跨比、轴压比、弯剪比;Among them, there are 6 nodes in the input layer, and the 6 nodes represent the stirrup ratio, longitudinal reinforcement ratio, ratio of stirrup spacing to section effective height, shear-span ratio, axial compression ratio, and bending-shear ratio;
其中,输入层激活函数的表达式为:Among them, the expression of the input layer activation function is:
y=f(Wp+b)y=f(Wp+b)
其中,y为激活函数的输出向量;W为权重矩阵;p为初始输入向量;b为偏置向量。Among them, y is the output vector of the activation function; W is the weight matrix; p is the initial input vector; b is the bias vector.
隐藏层包括两层,第一层有100个节点,第二层有10个节点;其中,隐藏层激活函数为sigmoid函数。The hidden layer includes two layers, the first layer has 100 nodes, and the second layer has 10 nodes; wherein, the activation function of the hidden layer is a sigmoid function.
sigmoid函数的表达式为:The expression of the sigmoid function is:
其中,f(x)为sigmoid函数的输出值;x为输入变量;e为自然常数。Among them, f(x) is the output value of the sigmoid function; x is the input variable; e is a natural constant.
输出层节点数为3,其中每个节点对应一种破坏模式;其中输出层激活函数为softmax函数。The number of nodes in the output layer is 3, and each node corresponds to a damage mode; the activation function of the output layer is the softmax function.
softmax函数的表达式为:The expression of the softmax function is:
其中,softmax(x)为softmax函数的输出值;e为自然常数;xi为第i个输入变量;xj为第j个输入变量;n为输入变量的数量。Among them, softmax(x) is the output value of the softmax function; e is a natural constant; x i is the i-th input variable; x j is the j-th input variable; n is the number of input variables.
请参阅图1,图1为人工神经网络结构的示意图,也即为ANN结构示意图。Please refer to FIG. 1 . FIG. 1 is a schematic diagram of an artificial neural network structure, that is, a schematic diagram of an ANN structure.
其中,Levenberg Marquardt反向传播训练算法的表达式为:Among them, the expression of the Levenberg Marquardt backpropagation training algorithm is:
△x=-[JTJ+μI]-1JTε△x=-[J T J+μI] -1 J T ε
其中,J为雅克比矩阵;JT为雅克比矩阵J的转置矩阵;μ为正常数;I为单位矩阵;ε为网络误差。Among them, J is the Jacobian matrix; J T is the transpose matrix of the Jacobian matrix J; μ is a normal number; I is the identity matrix; ε is the network error.
当μ为0时,该Levenberg Marquardt反向传播训练算法即为牛顿法;当μ的取值越大,则Levenberg Marquardt反向传播训练算法接近于梯度下降法。When μ is 0, the Levenberg-Marquardt backpropagation training algorithm is Newton's method; when the value of μ is larger, the Levenberg-Marquardt backpropagation training algorithm is close to the gradient descent method.
在对人工神经网络模型经过测试后,可以发现在没有标准化或归一化数据的情况下,训练的模型产生了更好的结果。可能是输入参数尺度相对接近,并且对于一种破坏模式,数据量相对稀缺。因此,如果数据集是标准化的,则可能会失去对此破坏模式的一些敏感性。After testing the artificial neural network model, it was found that the model trained without normalization or normalization of the data produced better results. It may be that the input parameter scales are relatively close, and for a failure mode, the amount of data is relatively scarce. Therefore, some sensitivity to this corruption mode may be lost if the dataset is normalized.
请参阅图2~图7,图2为配箍率对破坏模式影响的箱线图;图3为纵向配筋率对破坏模式影响的箱线图;图4为箍筋间距与截面有效高度比对破坏模式影响的箱线图;图5为剪跨比对破坏模式影响的箱线图;图6为轴压比对破坏模式影响的箱线图;图7为弯剪比对破坏模式影响的箱线图,图2~图7分别为配箍率、纵向配筋率、箍筋间距与截面有效高度比、剪跨比、轴压比、弯剪比这六个输入参数对破坏模式的定性影响。图2~图7的横轴均为破坏模式,其中图2~图7的横轴中1均代表弯曲破坏模式,横轴中的2均代表弯曲-剪切破坏模式,横轴中的3均代表剪切破坏模式;图2中纵轴为配箍率;图3中的纵轴为纵向配筋率;图4中的纵轴为箍筋间距与截面有效高度比;图5中纵轴为剪跨比;图6中纵轴为轴压比;图7中纵轴为弯剪比。Please refer to Figures 2 to 7. Figure 2 is the box-line diagram of the effect of the ratio of stirrups on the failure mode; Figure 3 is the box-line diagram of the effect of the ratio of longitudinal reinforcement on the failure mode; Figure 4 is the ratio of the spacing of the stirrups to the effective height of the section The boxplot of the influence on the failure mode; Figure 5 is the boxplot of the influence of the shear-span ratio on the failure mode; Figure 6 is the boxplot of the influence of the axial compression ratio on the failure mode; Figure 7 is the influence of the bending-shear ratio on the failure mode Box plots, Figures 2 to 7 are the qualitative analysis of the failure mode by the six input parameters of stirrup ratio, longitudinal reinforcement ratio, ratio of stirrup spacing to section effective height, shear-span ratio, axial compression ratio, and bending-shear ratio Influence. The horizontal axes of Figures 2 to 7 are failure modes, where 1 in the horizontal axes of Figures 2 to 7 represents the bending failure mode, 2 in the horizontal axis represents the bending-shear failure mode, and 3 in the horizontal axis represents the failure mode. Represents the shear failure mode; the vertical axis in Figure 2 is the stirrup ratio; the vertical axis in Figure 3 is the longitudinal reinforcement ratio; the vertical axis in Figure 4 is the ratio of the stirrup spacing to the section effective height; the vertical axis in Figure 5 is Shear-span ratio; the vertical axis in Figure 6 is the axial compression ratio; the vertical axis in Figure 7 is the bending-shear ratio.
请参阅图8,图8为Pearson相关系数矩阵,图8反映了Pearson相关系数矩阵定量分析每个参数对破坏模式的影响;图8中ρ"为配箍率;ρl为纵向配筋率;s/d为箍筋间距与截面有效高度比;a/d为剪跨比;P/Ag*fc'为轴压比;Vp/Vn为弯剪比。由图8中坐标轴上最下方的数据可以看出,弯剪比(Vp/Vn)和剪跨比(a/d)与钢筋混凝土矩形柱构件破环模式相对相关。与弯剪比(Vp/Vn)和剪跨比(a/d)比较,配箍率(ρ")、纵向配筋率(ρl)、轴压比(P/Ag*fc'),以及箍筋间距与截面有效高度比(s/d)对破坏模式没有显著影响。Please refer to Figure 8, Figure 8 is the Pearson correlation coefficient matrix, and Figure 8 reflects the impact of each parameter on the failure mode in the quantitative analysis of the Pearson correlation coefficient matrix; in Figure 8, ρ" is the stirrup ratio; ρ l is the longitudinal reinforcement ratio; s/d is the ratio of the stirrup spacing to the effective height of the section; a/d is the shear-span ratio; P/A g *f c ' is the axial compression ratio; V p /V n is the bending-shear ratio. From the data at the bottom of the figure, it can be seen that the bending-shear ratio (V p /V n ) and the shear-span ratio (a/d) are relatively related to the failure mode of reinforced concrete rectangular column members. The bending-shear ratio (V p /V n ) and shear-span ratio (a/d), stirrup ratio (ρ"), longitudinal reinforcement ratio (ρ l ), axial compression ratio (P/A g *f c '), and stirrup spacing and section effective The height ratio (s/d) has no significant effect on the failure mode.
在表1的111组数据中,取89组作为模型训练数据使用,剩下22组作为测试数据。模型优化后,训练数据和测试数据准确率分别达到100%和95.3%,也即使得训练好的人工神经网络的训练数据的准确率达到100%、测试数据的准确率达到95.3%。训练数据最小均方误差(MSE)为0.0018,测试数据最小均方误差(MSE)为0.038。请参阅图9和图10,图9为数据预测准确率的示意图,图10为最小均方误差的示意图,其中图9和图10的横轴均为迭代次数。Among the 111 sets of data in Table 1, 89 sets are used as model training data, and the remaining 22 sets are used as test data. After the model is optimized, the accuracy of the training data and test data reaches 100% and 95.3% respectively, which means that the accuracy of the training data of the trained artificial neural network reaches 100%, and the accuracy of the test data reaches 95.3%. The minimum mean square error (MSE) of the training data is 0.0018, and the minimum mean square error (MSE) of the test data is 0.038. Please refer to Figure 9 and Figure 10, Figure 9 is a schematic diagram of data prediction accuracy, Figure 10 is a schematic diagram of the minimum mean square error, where the horizontal axis of Figure 9 and Figure 10 is the number of iterations.
如表1所示,表1为矩形柱的参数数据和破坏模式。As shown in Table 1, Table 1 shows the parameter data and failure mode of the rectangular column.
表1Table 1
其中,FM表示随机变量地震破坏模式。Among them, FM represents the random variable earthquake damage mode.
请参阅图11,图11为混淆矩阵的示意图,根据图11中的混淆矩阵所示,在22个预测结果中,有1个预测错误,1个“弯曲-剪切破坏”模式被错误地判别为“剪切破坏”模式。Please refer to Figure 11. Figure 11 is a schematic diagram of the confusion matrix. According to the confusion matrix in Figure 11, among the 22 prediction results, there is 1 prediction error, and 1 "bending-shear failure" mode is wrongly identified For "shear failure" mode.
预测结果汇总于表2中,表2的详细说明如下:The prediction results are summarized in Table 2, and the details of Table 2 are as follows:
(1)在发生弯曲破坏的13组数据中,所有数据均被正确地预测为弯曲破坏。(1) Among the 13 sets of data where bending failure occurred, all the data were correctly predicted as bending failure.
(2)在发生弯曲-剪切破坏的7组数据中,有6组数据被正确地预测为弯曲-剪切破坏,1组数据被错误地预测为剪切破坏。(2) Among the 7 sets of data in which bending-shear failure occurred, 6 sets of data were correctly predicted as bending-shear failure, and 1 set of data was wrongly predicted as shear failure.
(3)在发生剪切破坏的2组数据中,所有数据均被正确地预测为剪切破坏。(3) In the 2 sets of data where shear failure occurred, all the data were correctly predicted as shear failure.
表2Table 2
预测结果的统计分析列于表3中。The statistical analysis of the predicted results is listed in Table 3.
表3table 3
由预测结果的统计性分析可知,95.3%(95.3%=(100%+86%+100%)/3)的柱构件被正确地预测。From the statistical analysis of the prediction results, it was found that 95.3% (95.3%=(100%+86%+100%)/3) of the column members were correctly predicted.
在基于剪跨比的方法中,柱构件的破坏模式仅与剪跨比有关。当剪跨比λ=a/d≤2时,这种破坏模式划分为剪切破坏;当剪跨比λ=a/d≥4时,这种破坏模式划分为弯曲破坏;当2<a/d<4时,这种破坏模式划分为弯剪破坏。其中,a表示为剪跨跨长,d表示为截面有效高度。In the shear-span ratio-based method, the failure mode of the column member is only related to the shear-span ratio. When the shear-span ratio λ=a/d≤2, this failure mode is classified as shear failure; when the shear-span ratio λ=a/d≥4, this failure mode is classified as bending failure; when 2<a/d When d<4, this failure mode is classified as bending-shear failure. Among them, a represents the span length of the shear span, and d represents the effective height of the section.
当剪跨比为λ=a/d≤2时,63%的柱构件发生剪切破坏;当剪跨比为λ=a/d≥4"时,51%的柱构件发生弯曲破坏;当剪跨比为2<a/d<4时,92%的柱构件发生弯曲-剪切破坏。When the shear-span ratio is λ=a/d≤2, 63% of the column members undergo shear failure; when the shear-span ratio is λ=a/d≥4", 51% of the column members undergo bending failure; when the shear-span ratio When the span ratio is 2<a/d<4, 92% of the column members suffer bending-shear failure.
结果表明,68.7%(68.7%=(63%+51%+92%)/3)的柱构件被正确地预测。这也说明λ=a/d=2和λ=a/d=4的剪跨比不足以区分构件的不同破坏模式。因此,仅依靠剪跨比来划分破坏模式是不恰当的。The results showed that 68.7% (68.7%=(63%+51%+92%)/3) of the column members were correctly predicted. This also shows that the shear-span ratios of λ=a/d=2 and λ=a/d=4 are not enough to distinguish different failure modes of components. Therefore, it is inappropriate to divide the failure mode only by shear-span ratio.
判别分析法包含参数法和非参数法。参数法假定每类的观测来自多元正态分布总体,各类的分布均值中心可以不同。非参数法不需知道各类来自总体的分布,它对每一类使用非参数方法,并且估计每一类的分布密度,然后据此建立判别准则。Discriminant analysis includes parametric and non-parametric methods. The parametric method assumes that the observations of each class come from a multivariate normal distribution population, and the distribution mean center of each class can be different. The non-parametric method does not need to know the distribution of each class from the population. It uses a non-parametric method for each class and estimates the distribution density of each class, and then establishes a criterion based on this.
判别分析法是基于费雪准则(Fisher criterion)并结合贝叶斯准则(Bayescriterion)对111个钢筋混凝土矩形柱构件的破坏模式进行判别,则可以得到三个判别方程,如下式所示。判别方程是线性统计方程,使用箍筋间距与截面有效高度比(χ)、剪跨比(λ))和弯剪比(m)来计算三个独立输出变量值:y1、y2和y3。根据y1、y2和y3的相对值,对钢筋混凝土柱破坏模式进行预测。如果y1最大,则钢筋混凝土柱破坏为弯曲破坏。如果y2最大,则钢筋混凝土柱破坏为弯曲-剪切破坏。如果y3最大,则钢筋混凝土柱破坏为剪切破坏。判别方程的系数代表权重。可以看出,弯剪比系数最大,说明判别方程对弯剪比的值最敏感。这说明弯剪比可以在一定程度上反映钢筋混凝土柱的破坏模式。这就是为什么在使用单个参数分析时,弯剪比可以比其他参数更准确的原因。但是,其他参数也不容忽视。The discriminant analysis method is based on the Fisher criterion combined with the Bayes criterion to discriminate the failure modes of 111 reinforced concrete rectangular column members, and then three discriminant equations can be obtained, as shown in the following formula. The discriminant equation is a linear statistical equation that uses the ratio of stirrup spacing to section effective height (χ), shear-span ratio (λ) and bending-shear ratio (m) to calculate the values of three independent output variables: y 1 , y 2 and y 3 . Based on the relative values of y 1 , y 2 and y 3 , the failure mode of the reinforced concrete column is predicted. If y1 is the largest, the failure of the reinforced concrete column is bending failure. If y2 is the largest, the failure of the reinforced concrete column is bending-shear failure. If y3 is the largest, the failure of the reinforced concrete column is shear failure. The coefficients of the discriminant equation represent weights. It can be seen that the coefficient of the bending-shear ratio is the largest, indicating that the discriminant equation is most sensitive to the value of the bending-shear ratio. This shows that the bending-shear ratio can reflect the failure mode of reinforced concrete columns to a certain extent. This is why the bending-shear ratio can be more accurate than the other parameters when analyzed using a single parameter. However, other parameters cannot be ignored.
y1=-7.664χ+6.448λ+16.86m-19.455y 1 =-7.664χ+6.448λ+16.86m-19.455
y2=-0.168χ+4.942λ+21.232m-20.815y 2 =-0.168χ+4.942λ+21.232m-20.815
y3=-2.935χ+4.038λ+25.726m-23.226y 3 =-2.935χ+4.038λ+25.726m-23.226
其中,y1、y2和y3均为独立输出变量值;χ为箍筋间距与截面有效高度比;λ为剪跨比;m为弯剪比。Among them, y 1 , y 2 and y 3 are independent output variable values; χ is the ratio of the stirrup spacing to the effective height of the section; λ is the shear-span ratio; m is the bending-shear ratio.
基于判别方程的预测方法的结果列于表4。表4的详细说明如下:The results of the prediction method based on the discriminant equation are listed in Table 4. The detailed description of Table 4 is as follows:
(1)在发生弯曲破坏的64组数据中,有59组数据被正确地预测为弯曲破坏,有5组数据被错误地预测为弯曲-剪切破坏。(1) Among the 64 sets of data where bending failure occurred, 59 sets of data were correctly predicted as bending failure, and 5 sets of data were wrongly predicted as bending-shear failure.
(2)在发生弯曲-剪切破坏的36组数据中,有26组数据被正确地预测为弯曲-剪切破坏,5组数据被错误地预测为弯曲破坏,5组数据被错误地预测为剪切破坏。(2) Among the 36 sets of data in which bending-shear failure occurred, 26 sets of data were correctly predicted as bending-shear failure, 5 sets of data were wrongly predicted as bending failure, and 5 sets of data were wrongly predicted as Shear failure.
(3)在11组发生剪切破坏的数据中,10组数据被正确地预测为剪切破坏,1组数据被错误地预测为弯曲-剪切破坏。(3) Among the 11 sets of data with shear failure, 10 sets of data were correctly predicted as shear failure, and 1 set of data was wrongly predicted as bending-shear failure.
表4Table 4
可以发现通过判别分析法,85.1%(85.1%=(92.2%+72.2%+90.9%)/3)的柱构件被正确地预测。它的准确度远高于其他只采用单一参数预测方法。It was found that 85.1% (85.1%=(92.2%+72.2%+90.9%)/3) of the column members were correctly predicted by the discriminant analysis. Its accuracy is much higher than other forecasting methods that only use a single parameter.
通过综合分析上述判别分析法,可知配箍率、轴压比、纵向配筋率、箍筋间距与截面有效高度比对柱构件破坏模式均没有显著影响。对柱构件破坏模式影响最大的两个参数是弯剪比和剪跨比。请参阅图12,图12为基于弯剪比和剪跨比的破坏模式预测的示意图,将这111个矩形柱构件的破坏模式按弯剪比和剪跨比进行划分,12中横轴为剪跨比,纵轴为折减弯剪比。Through the comprehensive analysis of the above discriminant analysis method, it can be seen that the ratio of stirrups, axial compression ratio, longitudinal reinforcement ratio, stirrup spacing and section effective height ratio have no significant impact on the failure mode of column members. The two parameters that have the greatest influence on the failure mode of column members are the bending-shear ratio and the shear-span ratio. Please refer to Figure 12. Figure 12 is a schematic diagram of failure mode prediction based on the bending-shear ratio and shear-span ratio. The failure modes of these 111 rectangular column members are divided according to the bending-shear ratio and shear-span ratio. Span ratio, the vertical axis is the reduced bending-shear ratio.
基于图12,可以开发一种基于弯剪比和剪跨比手动预测柱构件破坏模式的快速简易方法——工程简化判别分析法。根据图12,可以使用以下准则对钢筋混凝土柱的破坏模式进行预测。Based on Figure 12, a fast and simple method for manually predicting the failure mode of column members based on the bending-shear ratio and shear-span ratio can be developed—the engineering simplified discriminant analysis method. According to Fig. 12, the failure modes of RC columns can be predicted using the following criteria.
(1)对于剪跨比λ≤2的柱构件,当弯剪比Vp/Vn≥0.8,时,以剪切破坏为主;当弯剪比小于Vp/Vn<0.8时,以弯曲-剪切破坏为主。(1) For column members with shear-span ratio λ≤2, when the bending-shear ratio V p /V n ≥ 0.8, the shear failure is dominant; when the bending-shear ratio is less than V p /V n <0.8, the Bending-shear failure is dominant.
(2)对于剪跨比2<λ<4的柱构件,当弯剪比Vp/Vn<0.8时,以弯曲破坏为主;当弯剪比0.8≤Vp/Vn≤1.5时,以弯曲-剪切破坏为主;当Vp/Vn>1.5,柱构件发生剪切破坏。(2) For column members with a shear-span ratio of 2<λ<4, when the bending-shear ratio V p /V n <0.8, bending failure is dominant; when the bending-shear ratio is 0.8≤V p /V n ≤1.5, Bending-shear failure is the main form; when V p /V n >1.5, shear failure occurs in column members.
(3)对于剪跨比λ≥4的柱构件,当弯剪比Vp/Vn≤1.2时,以弯曲破坏为主;当弯剪比Vp/Vn>1.2时,此时因缺少样本无法得出任何结论。(3) For column members with a shear-span ratio λ≥4, when the bending-shear ratio V p /V n ≤ 1.2, bending failure is dominant; when the bending-shear ratio V p /V n > 1.2, due to the lack No conclusions can be drawn from the sample.
柱构件破坏模式预测准则总结在表5中。The failure mode prediction criteria for column members are summarized in Table 5.
表5table 5
基于表5中预测准则而得出的预测结果列于表6中。表6的详细说明如下:The prediction results based on the prediction criteria in Table 5 are listed in Table 6. The detailed description of Table 6 is as follows:
(1)在发生弯曲破坏的64组数据中,有49组数据被正确地预测为弯曲破坏,有15组数据被错误地预测为弯曲-剪切破坏。(1) Among the 64 sets of data in which bending failure occurred, 49 sets of data were correctly predicted as bending failure, and 15 sets of data were wrongly predicted as bending-shear failure.
(2)在发生弯曲-剪切破坏的36组数据中,有31组数据被正确地预测为弯曲-剪切破坏,2组数据被错误地预测为弯曲破坏,3组数据被错误地预测为剪切破坏。(2) Among the 36 sets of data in which bending-shear failure occurred, 31 sets of data were correctly predicted as bending-shear failure, 2 sets of data were wrongly predicted as bending failure, and 3 sets of data were wrongly predicted as Shear failure.
(3)在11组发生剪切破坏的数据中,10组数据被正确地预测为剪切破坏,1组数据被错误地预测为弯曲-剪切破坏。(3) Among the 11 sets of data with shear failure, 10 sets of data were correctly predicted as shear failure, and 1 set of data was wrongly predicted as bending-shear failure.
表6Table 6
由此可知,工程简化判别分析法对84.5%(84.5%=(76.6%+86.1%+90.9%)/3)的柱构件进行了正确预测,略低于判别分析法的准确率。It can be seen that the engineering simplified discriminant analysis method correctly predicts 84.5% (84.5% = (76.6% + 86.1% + 90.9%) / 3) column members, which is slightly lower than the accuracy rate of the discriminant analysis method.
本发明与传统预测方法对比,ANN网络预测方法有如下优点:The present invention compares with traditional prediction method, and ANN network prediction method has following advantages:
(1)ANN网络预测方法的准确率比传统预测方法要高。在传统预测方法中,基于判别分析的预测方法的准确率是最高的,达到85.1%,而ANN网络的预测方法的准确率高达95.3%。(1) The accuracy of the ANN network prediction method is higher than that of the traditional prediction method. Among the traditional prediction methods, the accuracy rate of the prediction method based on discriminant analysis is the highest, reaching 85.1%, while the accuracy rate of the ANN network prediction method is as high as 95.3%.
(2)ANN网络的预测方法考虑的因素更为全面。例如,基于剪跨比的预测方法只考虑单一参数,基于工程简化判别分析的预测方法考虑了2个参数,基于判别分析的预测方法考虑了3个参数,而ANN网络的预测方法则考虑了6个参数。(2) The prediction method of ANN network considers more comprehensive factors. For example, the prediction method based on shear-span ratio only considers a single parameter, the prediction method based on engineering simplified discriminant analysis considers 2 parameters, the prediction method based on discriminant analysis considers 3 parameters, and the prediction method of ANN network considers 6 parameters.
(3)随着数据库的扩展,模型的预测能力可以动态提高。(3) With the expansion of the database, the prediction ability of the model can be dynamically improved.
本实施例基于人工神经网络的预测方法,结合Levenberg Marquardt反向传播训练算法来判别矩形柱构件破坏模式。首先,设置钢筋混凝土矩形柱构件破坏模式的人工神经网络结构;对矩形柱构件的数据集进行处理,对影响矩形柱构件破坏模式中的配箍率、纵向配筋率、箍筋间距与截面有效高度比、剪跨比、轴压比、弯剪比进行敏感性分析,得到矩形柱构件破坏模式预测结果;对矩形柱构件破坏模式预测结果进行统计性分析。This embodiment is based on the artificial neural network prediction method, combined with the Levenberg Marquardt backpropagation training algorithm to identify the failure mode of the rectangular column member. First, the artificial neural network structure of the failure mode of reinforced concrete rectangular column members is set; the data set of rectangular column members is processed, which is effective for affecting the stirrup ratio, longitudinal reinforcement ratio, stirrup spacing and cross-section in the failure mode of rectangular column members Sensitivity analysis of height ratio, shear-span ratio, axial compression ratio, and bending-shear ratio is carried out to obtain the failure mode prediction results of rectangular column members; statistical analysis is carried out on the failure mode prediction results of rectangular column members.
需要说明的是:以上所述仅为本发明的较佳实施例,并不用以限制本发明,凡在本发明的原则之内,所作的任何修改、等同替换、改进等,均应包含在本发明的保护范围之内。It should be noted that: the above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the principles of the present invention shall be included in the present invention. within the scope of protection of the invention.
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