机敏混凝土结构的电阻率层析成像研究
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摘要
电阻率层析成像(Electric Resistance Tomography，简称ERT)由于具有非侵入性、在线、无放射性、结构简单、设备成本低廉、设备搬运灵活、响应快速、监测结果直观、监测信息量大等优点，在医学、地球物理勘探、水文结构探测等领域得到了广泛应用。但在混凝土结构中的应用尚未见有报道，其主要原因是混凝土本身的电阻率太大且不稳定。在混凝土中加入少量碳纤维形成的机敏混凝土(Carbon Fiber Reinfored Concrete，简称CFRC)具有导电性和压敏性，由此使得ERT技术应用于混凝土结构成像监测成为可能。
本文提出了用ERT技术对CFRC结构进行成像监测的新方法。该方法通过对CFRC结构表面电流、电压的施加和测量来获得携带其内部电阻率分布信息的投影数据，再利用反演计算方法重建出反映结构内部物质构成和状态的电阻率分布图，从而实现对CFRC结构的状态监测。
在对ERT基本原理和相关理论进行全面系统分析的基础上，深入研究了ERT技术在CFRC结构监测中应用的相关问题。主要创新工作如下：
1．提出了一种ERT测量(投影)方法。与其它投影方法不同，该方法测量的所有测量参考点都选在低电势的激励电极上，测量系统采集时将所有激励和测量电极的电位(参考点为0V)都采集到计算机内，并按编号记录各电极测量值。这种测量方法简化了测量系统结构，用较简单的存储结构实现了电压激励条件和响应结果数据的完备记录。
2．开发设计了一种复杂电阻率分布的ERT数值投影方法，实现了CFRC结构ERT的测量模拟。通过参数化孔洞模型的建立、计算机辅助建模软件开发和程序自动生成技术研究，实现了在ANSYS中的任意复杂电阻率分布的有限元模型建立、载荷变换、求解和投影数据记录等数值投影操作的自动处理功能，解决了在ANSYS中进行交互方式ERT测量数值模拟的工作量庞大、投影周期长和容易出错等问题。
3．提出了一种基于物理模型的ERT图像重建算法—等位线修正算法。该方法通过将等位线划分区域的各单元未知量组合为一个整体处理，实现了未知量的降维，使得单次激励的ERT不适定反问题转化为ERT适定反问题，提高解的稳定性。当换用另一次激励时，由于等位线划分区域不同，因而各单元未知量的组合方法也不同，这种动态降维方法允许ERT有限元单元个数超过独立测量数据个数，实现了较高空间分辨率的ERT图像稳定重建。与非反投影类算法相比，该方法不需要求解Jacobi矩阵和Hessian矩阵，不需要正则化方法，具有算法原理直观、速度快、求解稳定和精度高等特点；与一般反投影类算法相比，该方法由于可进行多次等位线修正的迭代，因而图像重建精度较高。
4．研制了CFRC结构的ERT软硬件系统。本文在对ERT基本原理和关键理论进行全面系统研究的基础上，首次研制了一套应用于CFRC结构监测的ERT软硬件系统。该系统由ERT投影测量软硬件子系统、ERT系统配置模块、ERT投影模型定义模块、ERT重建模型定义模块、ERT图像重建模块和图像显示处理模块等组成。该系统的研制为进一步的CFRC结构ERT研究提供了一个独立且完整的平台。
5．进行了多种截面形状结构和非均匀电极布置的ERT研究。目前ERT的研究对象截面形状往往比较确定，其ERT电极一般都采用均匀布置方式。如地球物理勘探的ERT测试对象为大地，截面形状为半无限空间，ERT电极采用等间距布置；工业流型监测的ERT测试对象为工业管道，截面形状为圆形，ERT电极采用均匀布置在管道圆周上。本文利用所研制的ERT系统进行了多种截面形状(包括方形截面ERT、长条形路面ERT和几种异形截面ERT)和不同电极布置方式的ERT仿真研究。研究结果表明：各种截面形状ERT成像效果良好，恰当地布置ERT电极可以提高局部成像分辨率。此外，本文还通过CFRC试件的ERT实验对ERT技术应用于CFRC结构监测的可行性和所做的ERT研究的正确性进行了验证。
This paper, study on Electrical Resistance Tomographic (ERT) of Carbon Fiber Reinforced Concrete (CFRC) structure, is sponsored by the National Natural Science Foundation of China (No. 50238040).
ERT method has many advantages, such as non-intrusion, online property, no-radioactivity, simpleness, inexpensiveness, portability, fast respond, result understandability and having mass of information of the result. This technology has been applied on physic, earth reconnoiter and hydrology. So far, no usage of ERT of concrete structure monitoring has been reported yet, because the resistivity of is very hight and not steatbale. CFRC, which is a kind of cement containing a small amount of short carbon fibers and has the properity of conductivity and pressure sensitivity, make it possible to monitor the CFRC structure by ERT method.
This paper put forward a new method of monitoring CFRC structure by ERT technology. ERT aims to reconstruct the conducting ( or dielectric) properties of an object from measurements of the electrical signals measured from all possible sensing electrodes while an exciting current or voltage is exerted to the object throught a pair of sensing electrodes mounted on the sufface of it. Therefore, the spatial gradients of electrical conductivity, which are a function of damage or strain gradients, can be measured.
The correlative matters about the applications of ERT of CFRC structure monitoring are studied, and the main innovatory work are listed as follow:
1. A new projection method of ERT is put forward in this paper. Compare to other ERT projection methods, all measurements of voltages are token the potential of the lower one of the pair of exciting electrodes potential as the same referent potential, and the voltages sampled from all the sensing electrodes (the voltage of referent electrode is 0V) are stored one by one according to the electrodes number in this method, which predigest the measure system, and achieve a maturity projection record of excited voltage and responed voltages with a compact storage stucture.
2. A numerical projection method used for complex resistivity distribution is proposed and designed. The author constructs parameterized hole-models and develops computer aided modeling software and ANSYS programs auto-generating software. Thus many functions of projection can be realized in ANSYS system automaticly, such as building the FEM model for complex resistivity distribution, changing loads, solving and recording data of projection, which resolves many important and difficult problems involved in using numerical projection method in ANSYS system, such as large mumbers of interactive manual operation, a long period of projection and high probability of making mistakes etc.
3. An image reconstructed algorithm called Contour Line Regulate (CLR) metdod based on physics model is put forward. In this method, all the unknown resisitivities of the elements in an area carved by contour lines are regarded as one unknown quantity, which would reduce the counts of unknown quantities and converted the ill-posed invert problem to a well one in the projection. In another projection, an alternant reducing method of the counts of unknown quantities is adopted because the contour lines are changed. This dynamic reducing method allows the counts of element great to the counts of independent datum, and a high resolution image is availabled. Compared to non-back projection reconstructed methods, the principle of this algorithm is simple. Jacobi matrix and Hessian matrix are not necessary and no regularization method is need in this algorithm. It has the advantages of high speed and steady. Compared to back projection reconstructed methods, because the CLR method is an iterative algorithm, it has high precision.
4. An ERT system of CFRC structure is developed. This paper does a full and detailed research on ERT. Based on researches of basic principles and pivotal theory, the author builds up a set of ERT system for CFRC structure monitoring for the first time. The system includes following modules: hardware and software system of ERT projection measurement, configurement module of ERT system, definition module of ERT projection model and ERT reconstruction model, ERT image reconstructed module and image processing module, etc. This system provides a whole set of independent hardware and software platform for the further research on ERT of CFRC structure.
5. The paper studies ERT technology of structures with different section shapes and ununiform electrodes arrangement. Recently ERT research groups generally do many reseach on ERT system with certain section shapes and uniform electrodes arrangement. Take physical reconnaissance of the globe for example, the earth is the research object. Its section shapes is semi-infinite space and ERT electrodes are equal spaced. The object of industry flow monitoring is pipes. Its section shape is circle and the electrodes are arranged uniformly.The paper researches the ERT system of structures with various section shapes, such as square, bar-shape and several heteromorphous section shapes, and ERT simulation is carried out for the structure with heteromorphous section shapes and ununiform electrode arrangement. The research results show that the ERT images of structures with all section shapes are satisfactory and appropriate ERT electrodes arrangement can enhance partial tomography resolution. Furthermore the feasibility of monitoring CFRC structure by ERT technology and the validity of the research are validated by experimentations.
本文提出了用ERT技术对CFRC结构进行成像监测的新方法。该方法通过对CFRC结构表面电流、电压的施加和测量来获得携带其内部电阻率分布信息的投影数据，再利用反演计算方法重建出反映结构内部物质构成和状态的电阻率分布图，从而实现对CFRC结构的状态监测。
在对ERT基本原理和相关理论进行全面系统分析的基础上，深入研究了ERT技术在CFRC结构监测中应用的相关问题。主要创新工作如下：
1．提出了一种ERT测量(投影)方法。与其它投影方法不同，该方法测量的所有测量参考点都选在低电势的激励电极上，测量系统采集时将所有激励和测量电极的电位(参考点为0V)都采集到计算机内，并按编号记录各电极测量值。这种测量方法简化了测量系统结构，用较简单的存储结构实现了电压激励条件和响应结果数据的完备记录。
2．开发设计了一种复杂电阻率分布的ERT数值投影方法，实现了CFRC结构ERT的测量模拟。通过参数化孔洞模型的建立、计算机辅助建模软件开发和程序自动生成技术研究，实现了在ANSYS中的任意复杂电阻率分布的有限元模型建立、载荷变换、求解和投影数据记录等数值投影操作的自动处理功能，解决了在ANSYS中进行交互方式ERT测量数值模拟的工作量庞大、投影周期长和容易出错等问题。
3．提出了一种基于物理模型的ERT图像重建算法—等位线修正算法。该方法通过将等位线划分区域的各单元未知量组合为一个整体处理，实现了未知量的降维，使得单次激励的ERT不适定反问题转化为ERT适定反问题，提高解的稳定性。当换用另一次激励时，由于等位线划分区域不同，因而各单元未知量的组合方法也不同，这种动态降维方法允许ERT有限元单元个数超过独立测量数据个数，实现了较高空间分辨率的ERT图像稳定重建。与非反投影类算法相比，该方法不需要求解Jacobi矩阵和Hessian矩阵，不需要正则化方法，具有算法原理直观、速度快、求解稳定和精度高等特点；与一般反投影类算法相比，该方法由于可进行多次等位线修正的迭代，因而图像重建精度较高。
4．研制了CFRC结构的ERT软硬件系统。本文在对ERT基本原理和关键理论进行全面系统研究的基础上，首次研制了一套应用于CFRC结构监测的ERT软硬件系统。该系统由ERT投影测量软硬件子系统、ERT系统配置模块、ERT投影模型定义模块、ERT重建模型定义模块、ERT图像重建模块和图像显示处理模块等组成。该系统的研制为进一步的CFRC结构ERT研究提供了一个独立且完整的平台。
5．进行了多种截面形状结构和非均匀电极布置的ERT研究。目前ERT的研究对象截面形状往往比较确定，其ERT电极一般都采用均匀布置方式。如地球物理勘探的ERT测试对象为大地，截面形状为半无限空间，ERT电极采用等间距布置；工业流型监测的ERT测试对象为工业管道，截面形状为圆形，ERT电极采用均匀布置在管道圆周上。本文利用所研制的ERT系统进行了多种截面形状(包括方形截面ERT、长条形路面ERT和几种异形截面ERT)和不同电极布置方式的ERT仿真研究。研究结果表明：各种截面形状ERT成像效果良好，恰当地布置ERT电极可以提高局部成像分辨率。此外，本文还通过CFRC试件的ERT实验对ERT技术应用于CFRC结构监测的可行性和所做的ERT研究的正确性进行了验证。
This paper, study on Electrical Resistance Tomographic (ERT) of Carbon Fiber Reinforced Concrete (CFRC) structure, is sponsored by the National Natural Science Foundation of China (No. 50238040).
ERT method has many advantages, such as non-intrusion, online property, no-radioactivity, simpleness, inexpensiveness, portability, fast respond, result understandability and having mass of information of the result. This technology has been applied on physic, earth reconnoiter and hydrology. So far, no usage of ERT of concrete structure monitoring has been reported yet, because the resistivity of is very hight and not steatbale. CFRC, which is a kind of cement containing a small amount of short carbon fibers and has the properity of conductivity and pressure sensitivity, make it possible to monitor the CFRC structure by ERT method.
This paper put forward a new method of monitoring CFRC structure by ERT technology. ERT aims to reconstruct the conducting ( or dielectric) properties of an object from measurements of the electrical signals measured from all possible sensing electrodes while an exciting current or voltage is exerted to the object throught a pair of sensing electrodes mounted on the sufface of it. Therefore, the spatial gradients of electrical conductivity, which are a function of damage or strain gradients, can be measured.
The correlative matters about the applications of ERT of CFRC structure monitoring are studied, and the main innovatory work are listed as follow:
1. A new projection method of ERT is put forward in this paper. Compare to other ERT projection methods, all measurements of voltages are token the potential of the lower one of the pair of exciting electrodes potential as the same referent potential, and the voltages sampled from all the sensing electrodes (the voltage of referent electrode is 0V) are stored one by one according to the electrodes number in this method, which predigest the measure system, and achieve a maturity projection record of excited voltage and responed voltages with a compact storage stucture.
2. A numerical projection method used for complex resistivity distribution is proposed and designed. The author constructs parameterized hole-models and develops computer aided modeling software and ANSYS programs auto-generating software. Thus many functions of projection can be realized in ANSYS system automaticly, such as building the FEM model for complex resistivity distribution, changing loads, solving and recording data of projection, which resolves many important and difficult problems involved in using numerical projection method in ANSYS system, such as large mumbers of interactive manual operation, a long period of projection and high probability of making mistakes etc.
3. An image reconstructed algorithm called Contour Line Regulate (CLR) metdod based on physics model is put forward. In this method, all the unknown resisitivities of the elements in an area carved by contour lines are regarded as one unknown quantity, which would reduce the counts of unknown quantities and converted the ill-posed invert problem to a well one in the projection. In another projection, an alternant reducing method of the counts of unknown quantities is adopted because the contour lines are changed. This dynamic reducing method allows the counts of element great to the counts of independent datum, and a high resolution image is availabled. Compared to non-back projection reconstructed methods, the principle of this algorithm is simple. Jacobi matrix and Hessian matrix are not necessary and no regularization method is need in this algorithm. It has the advantages of high speed and steady. Compared to back projection reconstructed methods, because the CLR method is an iterative algorithm, it has high precision.
4. An ERT system of CFRC structure is developed. This paper does a full and detailed research on ERT. Based on researches of basic principles and pivotal theory, the author builds up a set of ERT system for CFRC structure monitoring for the first time. The system includes following modules: hardware and software system of ERT projection measurement, configurement module of ERT system, definition module of ERT projection model and ERT reconstruction model, ERT image reconstructed module and image processing module, etc. This system provides a whole set of independent hardware and software platform for the further research on ERT of CFRC structure.
5. The paper studies ERT technology of structures with different section shapes and ununiform electrodes arrangement. Recently ERT research groups generally do many reseach on ERT system with certain section shapes and uniform electrodes arrangement. Take physical reconnaissance of the globe for example, the earth is the research object. Its section shapes is semi-infinite space and ERT electrodes are equal spaced. The object of industry flow monitoring is pipes. Its section shape is circle and the electrodes are arranged uniformly.The paper researches the ERT system of structures with various section shapes, such as square, bar-shape and several heteromorphous section shapes, and ERT simulation is carried out for the structure with heteromorphous section shapes and ununiform electrode arrangement. The research results show that the ERT images of structures with all section shapes are satisfactory and appropriate ERT electrodes arrangement can enhance partial tomography resolution. Furthermore the feasibility of monitoring CFRC structure by ERT technology and the validity of the research are validated by experimentations.
引文
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