钢筋混凝土受弯构件动力参数识别和损伤诊断研究
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摘要
提出本研究的意图是系统的动力性能研究及其应用,该研究可以概括为系统仿真和系统动力测试两部分,前者主要是理论研究,比如系统的动力模型、运动方程和解答,后者主要围绕实验展开,比如结构动力测试技术,系统参数识别方法。文章结合这两方面的问题展开,并着重在信号处理原理,参数识别方法上进行了深入探讨,对钢筋混凝土受弯构件进行了动力测试,依据测试数据识别得到结构的动力参数,总结测试技术和结构动力性能两方面的规律。研究的主要工作简述如下：
对钢筋混凝土受弯构件的分级静力加卸载性能进行了细致测试,得到构件随荷载增加刚度下降的真实变化曲线,结合相关研究推测构件弯曲刚度函数的主要特征,为理论研究和实际应用提供基本事实依据。首先只要当前荷载不大于结构经历过的最大荷载,受弯构件的荷载-挠度关系基本符合线性特征,依据动力测试数据识别结构动力参数,一般构件在荷载-挠度曲线上的非线性都比较弱,假设的结构模型与测试数据不符合时,多考虑其以外的其他因素,其次构件开裂截面上刚度下降所影响的区域也往往较小。
从傅立叶级数推导出离散傅立叶变换(DFT)表达式,对DFT物理意义进行了清晰完整的解释,采用不同的DFT表达式计算信号频谱时,只需相应调整频谱系数和频域坐标。在原理上澄清了频谱的对称性质,尽管有效谱线数N／2这个笼统的数字一般不会遗漏关键谱线,但有可能影响到对其他相关问题的理解,比如在频域计算过程中,会混淆数量关系；在讨论DFT物理意义的基础上进一步讨论了定频的改进方法：细化频谱分析。同时由理论推导发现了细化频谱与连续矩形窗频谱有极大相似之处,以连续矩形窗频谱曲线为样板,提出了一般保守信号细化频谱的量化特征,并在解决密集频率频谱的判定和分离的问题中得到应用。
通过细化频谱分析识别信号的频率和初相位,利用DFT的重要性质：离散卷积和反卷积原理。提出一种从自由衰减响应(FDR)中提取阻尼特性的新方法,本方法在对阻尼特性进行提取之前不需要对阻尼模型进行假设,提取FDR中各频率谐波的振幅随时间变化的时域序列,能够更加真实的揭示系统的阻尼特性,该方法主要对独立频率频谱比较适用。对于密集频率频谱,参考离散反卷积方法得到的识别结果,设定谐波参数范围和步长,把这些参数循环代入指定理论信号表达式中,寻找能使理论信号与实验信号的频域曲线最相近的参数组合确定为最优结果,实现了只用结构的响应信号识别系统模态参数的预想。
对钢筋混凝土框架、普通钢筋混凝土简支梁和组合梁进行了动力实验,依据对实验测试数据的计算结果,讨论了不同测试条件对测试结果的影响,总结了动力测试技术和结构的动力性能两方面的规律；在用动力方法对结构进行损伤诊断时,得到了模态参数随结构损伤的变化规律：各频率随损伤增加不断下降,其中高频的下降量较大,阻尼的指数衰减系数,在正常使用阶段也有随损伤增加而增加的趋势,高阶模态的趋势更大。频率和阻尼对判断结构的状态都有一定指示作用,而模态振型可以帮助判断重复模态。
The purpose of this dissertation is to solve the problems associated with dynamic performance of the system and its application. This study can be summarized as two parts:system simulation and system tests. The former part is mainly concerned with theoretical research, such as the dynamic model of the system, the establishment and the solution of the equation of motion. The latter part is mainly concerned with the experimentation, such as the test of structural dynamic characteristics, the system identification of structures. Two aspects are all discussed in the dissertation. Such as: the principle of digital signal processing (DSP) and the methods of parameters identification. Dynamic tests were carried out on reinforced concrete (RC) flexural members. According to the dynamic parameters of the members obtained from measured vibration responses, two aspects of the laws, as dynamic testing technique and structural dynamic performance, were summed up. The main works of the dissertation are presented as follows:
The loading-unloading performances were tested in detail on RC flexural member. The curves were gotten that described the changed trend of flexural stiffness with increasing load. The main features of flexural stiffness function were speculated as basic facts to support theoretical research and practical application. Firstly, as long as the current load is not greater than the maximum value of load that the member has been subjected to, load-deflection relationship of bending member will be in line with linear characteristics. While to identify the structural dynamic parameters based on dynamic measured data, it should be aware that non-linear of the load-deflection curve is very weak, the other factors will be considered in the case of conflict between the assumed structure model and the test data. Secondly, the area where the stiffness reduces due to cracking cross-section of member also tend to be smaller.
The discrete Fourier transform (DFT) was deduced from the Fourier series expression. And then the physical significance of DFT was explained clearly and completely. When the signal spectrum is calculated using the type of DFT expression, the spectral coefficients and the frequency domain coordinates need be adjusted correspondingly only. The symmetrical property of the spectrum was described in principle. Key spectral lines would not be missed generally in according to the general number N/2be considered as effective spectral lines. But the understanding of the related issues is likely to be affected. Such as the quantity relations might be confused in the process of calculation in frequency domain. Base on the discussion of DFT, the improved method that would visually extract the frequency as better peak of the spectrum, zoom spectrum analysis, was further discussed here. While it was discovered that a single frequency harmonic zoom spectrum and a rectangle window spectrum was very similar. Based on this law, the digital signal included several close frequency harmonics can be identified. Furthermore, Harmonic parameters can be extracted from the most close frequency digital signal.
Based on the identification of frequency and the initial phase using zoom spectral analysis and the important properties of the DFT. Discrete convolution and deconvolution principle, a new method was proposed for identifying the damping from free decay response (FDR) without dependency on a prior knowledge of damping model. The time sequence can be identified by discrete deconvolution technique which can be employed to reflect the changes of harmonic amplitude. The method is an excellent tool for the first estimation attempts. However, frequency resolution, leakage, coherence dropout at resonance, and the other factors make the peak amplitude susceptible to error and do not calculate the most accurate data. In that case, in according to the first results the appropriate parameter range and step size were selected for loop calculation. Next, in turn, these parameters would be substituted into the specified theoretical signal expression, the optimal results were determined on the principle to make spectrum curve of theoretical signal fit best with that of the experimental signal. As the original expectation, it is implemented that system parameters are identified using output data only.
Dynamic tests on RC frame, RC simply supported beam and composite beam have been performed to identify the system parameters using these measurements. The influences of test conditions were discussed. And the laws of dynamic testing techniques and the structural dynamic performance were summed up. When a structure is done by a damage diagnosis with the modal method, it can be listed below that Modal parameters change the rules:the frequencies will reduce while the damage of structure increases, meanwhile exponential decay coefficients is on the trend of increasing. The two parameters all have a larger trend in the high frequency harmonic. The frequency and damping are likely to be useful for detecting damage in RC structure. However modal shapes only can be used to determine the repetitive mode.
对钢筋混凝土受弯构件的分级静力加卸载性能进行了细致测试,得到构件随荷载增加刚度下降的真实变化曲线,结合相关研究推测构件弯曲刚度函数的主要特征,为理论研究和实际应用提供基本事实依据。首先只要当前荷载不大于结构经历过的最大荷载,受弯构件的荷载-挠度关系基本符合线性特征,依据动力测试数据识别结构动力参数,一般构件在荷载-挠度曲线上的非线性都比较弱,假设的结构模型与测试数据不符合时,多考虑其以外的其他因素,其次构件开裂截面上刚度下降所影响的区域也往往较小。
从傅立叶级数推导出离散傅立叶变换(DFT)表达式,对DFT物理意义进行了清晰完整的解释,采用不同的DFT表达式计算信号频谱时,只需相应调整频谱系数和频域坐标。在原理上澄清了频谱的对称性质,尽管有效谱线数N／2这个笼统的数字一般不会遗漏关键谱线,但有可能影响到对其他相关问题的理解,比如在频域计算过程中,会混淆数量关系；在讨论DFT物理意义的基础上进一步讨论了定频的改进方法：细化频谱分析。同时由理论推导发现了细化频谱与连续矩形窗频谱有极大相似之处,以连续矩形窗频谱曲线为样板,提出了一般保守信号细化频谱的量化特征,并在解决密集频率频谱的判定和分离的问题中得到应用。
通过细化频谱分析识别信号的频率和初相位,利用DFT的重要性质：离散卷积和反卷积原理。提出一种从自由衰减响应(FDR)中提取阻尼特性的新方法,本方法在对阻尼特性进行提取之前不需要对阻尼模型进行假设,提取FDR中各频率谐波的振幅随时间变化的时域序列,能够更加真实的揭示系统的阻尼特性,该方法主要对独立频率频谱比较适用。对于密集频率频谱,参考离散反卷积方法得到的识别结果,设定谐波参数范围和步长,把这些参数循环代入指定理论信号表达式中,寻找能使理论信号与实验信号的频域曲线最相近的参数组合确定为最优结果,实现了只用结构的响应信号识别系统模态参数的预想。
对钢筋混凝土框架、普通钢筋混凝土简支梁和组合梁进行了动力实验,依据对实验测试数据的计算结果,讨论了不同测试条件对测试结果的影响,总结了动力测试技术和结构的动力性能两方面的规律；在用动力方法对结构进行损伤诊断时,得到了模态参数随结构损伤的变化规律：各频率随损伤增加不断下降,其中高频的下降量较大,阻尼的指数衰减系数,在正常使用阶段也有随损伤增加而增加的趋势,高阶模态的趋势更大。频率和阻尼对判断结构的状态都有一定指示作用,而模态振型可以帮助判断重复模态。
The purpose of this dissertation is to solve the problems associated with dynamic performance of the system and its application. This study can be summarized as two parts:system simulation and system tests. The former part is mainly concerned with theoretical research, such as the dynamic model of the system, the establishment and the solution of the equation of motion. The latter part is mainly concerned with the experimentation, such as the test of structural dynamic characteristics, the system identification of structures. Two aspects are all discussed in the dissertation. Such as: the principle of digital signal processing (DSP) and the methods of parameters identification. Dynamic tests were carried out on reinforced concrete (RC) flexural members. According to the dynamic parameters of the members obtained from measured vibration responses, two aspects of the laws, as dynamic testing technique and structural dynamic performance, were summed up. The main works of the dissertation are presented as follows:
The loading-unloading performances were tested in detail on RC flexural member. The curves were gotten that described the changed trend of flexural stiffness with increasing load. The main features of flexural stiffness function were speculated as basic facts to support theoretical research and practical application. Firstly, as long as the current load is not greater than the maximum value of load that the member has been subjected to, load-deflection relationship of bending member will be in line with linear characteristics. While to identify the structural dynamic parameters based on dynamic measured data, it should be aware that non-linear of the load-deflection curve is very weak, the other factors will be considered in the case of conflict between the assumed structure model and the test data. Secondly, the area where the stiffness reduces due to cracking cross-section of member also tend to be smaller.
The discrete Fourier transform (DFT) was deduced from the Fourier series expression. And then the physical significance of DFT was explained clearly and completely. When the signal spectrum is calculated using the type of DFT expression, the spectral coefficients and the frequency domain coordinates need be adjusted correspondingly only. The symmetrical property of the spectrum was described in principle. Key spectral lines would not be missed generally in according to the general number N/2be considered as effective spectral lines. But the understanding of the related issues is likely to be affected. Such as the quantity relations might be confused in the process of calculation in frequency domain. Base on the discussion of DFT, the improved method that would visually extract the frequency as better peak of the spectrum, zoom spectrum analysis, was further discussed here. While it was discovered that a single frequency harmonic zoom spectrum and a rectangle window spectrum was very similar. Based on this law, the digital signal included several close frequency harmonics can be identified. Furthermore, Harmonic parameters can be extracted from the most close frequency digital signal.
Based on the identification of frequency and the initial phase using zoom spectral analysis and the important properties of the DFT. Discrete convolution and deconvolution principle, a new method was proposed for identifying the damping from free decay response (FDR) without dependency on a prior knowledge of damping model. The time sequence can be identified by discrete deconvolution technique which can be employed to reflect the changes of harmonic amplitude. The method is an excellent tool for the first estimation attempts. However, frequency resolution, leakage, coherence dropout at resonance, and the other factors make the peak amplitude susceptible to error and do not calculate the most accurate data. In that case, in according to the first results the appropriate parameter range and step size were selected for loop calculation. Next, in turn, these parameters would be substituted into the specified theoretical signal expression, the optimal results were determined on the principle to make spectrum curve of theoretical signal fit best with that of the experimental signal. As the original expectation, it is implemented that system parameters are identified using output data only.
Dynamic tests on RC frame, RC simply supported beam and composite beam have been performed to identify the system parameters using these measurements. The influences of test conditions were discussed. And the laws of dynamic testing techniques and the structural dynamic performance were summed up. When a structure is done by a damage diagnosis with the modal method, it can be listed below that Modal parameters change the rules:the frequencies will reduce while the damage of structure increases, meanwhile exponential decay coefficients is on the trend of increasing. The two parameters all have a larger trend in the high frequency harmonic. The frequency and damping are likely to be useful for detecting damage in RC structure. However modal shapes only can be used to determine the repetitive mode.
引文
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