基于“能量测试”和优化方法的结构单元损伤识别
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摘要
结构损伤识别也称为无损探伤技术,其主要研究内容是在不破坏现有结构的基础
上,采用各种试验手段对结构进行探测,并通过对测试结果的分析,确定结构的健康状
况。结构损伤识别要解决的问题主要有以下三个层次:(1) 、判断结构是否发生损伤;
(2) 、确定结构损伤产生的位置;(3) 、识别结构损伤的程度。
目前,国内外有很多已经发表的损伤识别方法应用到实际工程中,从磁粉、超声
波、X光以至于到工业CT技术,各式各样的测量手段在损伤识别问题中得到了广泛的应
用。而基于结构力学响应的损伤识别方法因其试验简单、费用低廉近20年来越来越受到
工程和学术界的关注。本文主要是就基于力学响应的损伤识别方法中存在的不足和缺陷
展开研究。现有的基于力学响应的损伤识别方法存在的主要问题有:(1) 、结构力学响应
相对于损伤参数的灵敏度较低:(2) 、识别结果的不适定性;(3) 、结构发生多处损伤
时,模型中未知变量过多导致优化方法失败等。
结构的力学响应主要包括静力响应、自振分析和强迫振动,在传统的损伤识别方法
中,不同的响应类型是按照不同的列式进行推导和计算的。本文提出了结构能量“测
试”的概念,将结构的各类力学响应(主要是目前应用最多的自振分析和静力响应)统
一起来,推导同样的列式,在损伤识别过程中只需得到结构的应变能,而不用考虑观测
数据的来源及其计算公式。仅从应变能的变化考虑如何提高结构响应对于损伤参数的灵
敏度。
为了克服结构力学响应相对于损伤参数灵敏度太低的问题,本文在能量测试的基础
上提出了“附加子系统”的思想,就是在测试结构上增加附加的外部系统,如外力、附加
质量块、附加支撑、阻尼等。通过这些“附加子系统”的引入,改变结构的应变能密度
分布情况,使得结构损伤部位的应变能密度极大化,从而提高损伤造成的结构力学响应
变化,实现提高结构力学响应相对于损伤参数灵敏度的目的。理论推导和数值算例表明
了方法的实用性和有效性。
结构的损伤不止一处时,如果将损伤描述成为结构单元刚度的变化,那么整个结构
的所有单元刚度都将成为损伤识别优化模型中的设计变量(待识别损伤参数),设计变
量的数目太多将导致结构优化方法失败;如果用损伤位置和损伤尺寸描述结构的损伤,
由于损伤数目无法确定,损伤识别的优化模型成为一个设计变量不定的离散结构优化问
题,目前还没有成熟的算法可以求解。本文引入一种新型损伤指示函数,首先确定结构
中损伤的数目,采用损伤处结构单元刚度降低描述损伤程度,以测试数据组合的损伤指
基于“能量测试”和优化方法的结构单元损伤识别
示函数和有限元模型计算损伤指示函数的最小二乘作为目标函数构造损伤识别问题的优
化模型,很好地解决了上述问题。
本文采用极大极小问题构造损伤识别的优化模型,通过凝聚函数将极大极小问题转
化为一个目标函数连续可微的无约束优化问题,采用基于灵敏度分析的序列线性规划方
法求解。为了考查方法的抗噪能力,在原始观测数据中引入随机误差,连续粱、板结构
的数值算例证明了方法的可行性和实用性。
最后,对全文工作进行了总结,并提出了需进一步研究的工作内容。
务
子“卜
、
产州曰
关键词:损伤识别,反问题,结构优化,能量“测试”,灵敏度分析,凝聚函数
Structural damage identification is a type of non-destructive detection technique. The main purpose of this technique is to determine the status of the structural health through analysis of the test results obtained using various experimental methods without destRictions to the existing structures. Three levels of problems can be dealt with structural damage identification, namely, (1) to judge if a structural damage exists; (2) to locate the positions of the damage; (3) to determine the extent of the damage.In the literatures, many damage identification methods have been applied in the practical engineering. A great variety of test techniques, such as magnetic power, ultrasonic wave, X-ray and industrial CT, have found wide applications in the structural damage identification problems. Particularly, the damage identification approach based on structural response changes have drawn much attention of both engineering and academic communities for the last two decades, due to its ease of implementation and low cost. This treatise is devoted to the study on avoiding the weakness and limitations of existing approaches based on response changes. The major difficulties of damage identification techniques relying on response changes are: (1) structural response are not sensitive enough with respect to the damage parameters; (2) the identification model are usually ill-posed; (3) the approaches using optimization techniques may fail in case of multiple damages as a result of too many variables in the mathematical model.Structural response includes static response, natural vibration properties and forced vibration response. In conventional damage identification methods, the problem is formulated in different ways according to the structural response adopted. In this research, the concept of structural energy "measurements" is proposed, thus different kinds of structural response are unified in the problem formulation. In this context, only the structural strain energy is needed in the derivation, regardless of the source of test data and the mathematical formula.To alleviate the difficulty caused by the insufficient sensitivities of the structural response to the damage parameters, the idea of "additional sub-system" is proposed, in which additional external system, such as external force, additional mass, additional supports, damping and similar, are attached to the structure to be tested. By this means, the distribution of the structural strain density is adjusted and the strain density in the vicinity of the damage position is maximized. As a result, the sensitivities of the response changes with respect to the damage are substantially increased. Theoretical derivations and numerical examples demonstrated the
applicability and the validity of the proposed method.For identification of multi-damages, the optimization approach may fail due to the extremely large number of design variables (parameters to be identified) if the damages are modeled as elemental stiffness changes and therefore all the elemental stiffness parameters in the finite element model become the design variables of the optimization model for the damage identification problem. On the other hand, if the damage position and the damage size are used for description of the structural damage, the mathematical model is actually stated as a discrete structural optimization problem with unknown number of design variables, since the number of damages can not be given in advance. Such a problem can not be easily solved. An approach is proposed in this treatise by introducing a new type of damage index function. The number of damages is firstly determined, and then, the stiffnesses decreases of structural elements are used as a description of the damage size. The least square of the damage index functions of the test data and the finite element prediction is used as the objective function of the optimization model for the damage identification. The difficulties mentioned above are therefore successfully avoided.The damage identification problem is formulated as a Min-ma
上,采用各种试验手段对结构进行探测,并通过对测试结果的分析,确定结构的健康状
况。结构损伤识别要解决的问题主要有以下三个层次:(1) 、判断结构是否发生损伤;
(2) 、确定结构损伤产生的位置;(3) 、识别结构损伤的程度。
目前,国内外有很多已经发表的损伤识别方法应用到实际工程中,从磁粉、超声
波、X光以至于到工业CT技术,各式各样的测量手段在损伤识别问题中得到了广泛的应
用。而基于结构力学响应的损伤识别方法因其试验简单、费用低廉近20年来越来越受到
工程和学术界的关注。本文主要是就基于力学响应的损伤识别方法中存在的不足和缺陷
展开研究。现有的基于力学响应的损伤识别方法存在的主要问题有:(1) 、结构力学响应
相对于损伤参数的灵敏度较低:(2) 、识别结果的不适定性;(3) 、结构发生多处损伤
时,模型中未知变量过多导致优化方法失败等。
结构的力学响应主要包括静力响应、自振分析和强迫振动,在传统的损伤识别方法
中,不同的响应类型是按照不同的列式进行推导和计算的。本文提出了结构能量“测
试”的概念,将结构的各类力学响应(主要是目前应用最多的自振分析和静力响应)统
一起来,推导同样的列式,在损伤识别过程中只需得到结构的应变能,而不用考虑观测
数据的来源及其计算公式。仅从应变能的变化考虑如何提高结构响应对于损伤参数的灵
敏度。
为了克服结构力学响应相对于损伤参数灵敏度太低的问题,本文在能量测试的基础
上提出了“附加子系统”的思想,就是在测试结构上增加附加的外部系统,如外力、附加
质量块、附加支撑、阻尼等。通过这些“附加子系统”的引入,改变结构的应变能密度
分布情况,使得结构损伤部位的应变能密度极大化,从而提高损伤造成的结构力学响应
变化,实现提高结构力学响应相对于损伤参数灵敏度的目的。理论推导和数值算例表明
了方法的实用性和有效性。
结构的损伤不止一处时,如果将损伤描述成为结构单元刚度的变化,那么整个结构
的所有单元刚度都将成为损伤识别优化模型中的设计变量(待识别损伤参数),设计变
量的数目太多将导致结构优化方法失败;如果用损伤位置和损伤尺寸描述结构的损伤,
由于损伤数目无法确定,损伤识别的优化模型成为一个设计变量不定的离散结构优化问
题,目前还没有成熟的算法可以求解。本文引入一种新型损伤指示函数,首先确定结构
中损伤的数目,采用损伤处结构单元刚度降低描述损伤程度,以测试数据组合的损伤指
基于“能量测试”和优化方法的结构单元损伤识别
示函数和有限元模型计算损伤指示函数的最小二乘作为目标函数构造损伤识别问题的优
化模型,很好地解决了上述问题。
本文采用极大极小问题构造损伤识别的优化模型,通过凝聚函数将极大极小问题转
化为一个目标函数连续可微的无约束优化问题,采用基于灵敏度分析的序列线性规划方
法求解。为了考查方法的抗噪能力,在原始观测数据中引入随机误差,连续粱、板结构
的数值算例证明了方法的可行性和实用性。
最后,对全文工作进行了总结,并提出了需进一步研究的工作内容。
务
子“卜
、
产州曰
关键词:损伤识别,反问题,结构优化,能量“测试”,灵敏度分析,凝聚函数
Structural damage identification is a type of non-destructive detection technique. The main purpose of this technique is to determine the status of the structural health through analysis of the test results obtained using various experimental methods without destRictions to the existing structures. Three levels of problems can be dealt with structural damage identification, namely, (1) to judge if a structural damage exists; (2) to locate the positions of the damage; (3) to determine the extent of the damage.In the literatures, many damage identification methods have been applied in the practical engineering. A great variety of test techniques, such as magnetic power, ultrasonic wave, X-ray and industrial CT, have found wide applications in the structural damage identification problems. Particularly, the damage identification approach based on structural response changes have drawn much attention of both engineering and academic communities for the last two decades, due to its ease of implementation and low cost. This treatise is devoted to the study on avoiding the weakness and limitations of existing approaches based on response changes. The major difficulties of damage identification techniques relying on response changes are: (1) structural response are not sensitive enough with respect to the damage parameters; (2) the identification model are usually ill-posed; (3) the approaches using optimization techniques may fail in case of multiple damages as a result of too many variables in the mathematical model.Structural response includes static response, natural vibration properties and forced vibration response. In conventional damage identification methods, the problem is formulated in different ways according to the structural response adopted. In this research, the concept of structural energy "measurements" is proposed, thus different kinds of structural response are unified in the problem formulation. In this context, only the structural strain energy is needed in the derivation, regardless of the source of test data and the mathematical formula.To alleviate the difficulty caused by the insufficient sensitivities of the structural response to the damage parameters, the idea of "additional sub-system" is proposed, in which additional external system, such as external force, additional mass, additional supports, damping and similar, are attached to the structure to be tested. By this means, the distribution of the structural strain density is adjusted and the strain density in the vicinity of the damage position is maximized. As a result, the sensitivities of the response changes with respect to the damage are substantially increased. Theoretical derivations and numerical examples demonstrated the
applicability and the validity of the proposed method.For identification of multi-damages, the optimization approach may fail due to the extremely large number of design variables (parameters to be identified) if the damages are modeled as elemental stiffness changes and therefore all the elemental stiffness parameters in the finite element model become the design variables of the optimization model for the damage identification problem. On the other hand, if the damage position and the damage size are used for description of the structural damage, the mathematical model is actually stated as a discrete structural optimization problem with unknown number of design variables, since the number of damages can not be given in advance. Such a problem can not be easily solved. An approach is proposed in this treatise by introducing a new type of damage index function. The number of damages is firstly determined, and then, the stiffnesses decreases of structural elements are used as a description of the damage size. The least square of the damage index functions of the test data and the finite element prediction is used as the objective function of the optimization model for the damage identification. The difficulties mentioned above are therefore successfully avoided.The damage identification problem is formulated as a Min-ma
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