工程结构模态参数辨识与损伤识别方法研究
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摘要
工程结构模态参数辨识与损伤识别技术作为近20年来适应工程实际需要而发展起来的一门新学科，有很强的工程背景，具有重要的实用价值。近些年来，工程结构的健康监测、损伤评估越来越受到人们的关注，而模态参数辨识和损伤识别作为其核心技术和理论基础已日益成为土木工程领域的研究热点。由于工程结构体积庞大、约束条件复杂、材料混杂等原因，对其进行人为激励以及对激励信号进行有效测量是相当困难的，因此，基于输入输出信号的传统模态参数识别理论和方法在工程结构中难以适用。而环境激励下的结构模态参数识别方法，具有无需施加人为激励、费用低廉、不影响结构的正常工作、无需测量激励信号、更加符合实际情况等优点，在工程界得到了广泛的应用。但现有的模态参数辨识方法和损伤识别方法在精度、鲁棒性、效率以及经济性能指标方面仍存在很多不足，在实际工程中的应用尚处于发展阶段，仍需进一步研究和完善。
针对目前研究中存在的问题，本文围绕环境激励下工程结构模态参数辨识方法和基于模态参数灵敏度的损伤识别方法开展研究，归结起来主要内容如下：
①计算三层钢筋砼框架模型在环境激励下的位移响应，利用两种数据预处理方法（随机减量法和NExT法）和ITD法、STD法、复指数法、ERA法和ARMA法等5种时域模态参数识别方法，开展了结构模态参数辨识的比较研究。结果表明：预处理方法中的NExT法在精度、抗噪性上均优于随机减量法；五种模态参数识别方法中STD法和ARMA法的对频率识别精度比其它三种方法稍高，在抗噪方面，STD、ERA法、ARMA法的抗噪能力比其它两种方法稍强，所有方法对频率的识别精度均远大于对阻尼比的识别精度。
②结合随机子空间法提出了环境激励下结构模态参数识别的改进ITD法、改进STD法与改进复指数法。随机子空间法的识别精度高，其中数据的协方差计算（矩阵正交投影计算）可以保留原始数据中的所有信息，同时去除了噪声，将得到的Toeplitz矩阵（P矩阵）中的数据作为ITD法、STD法与复指数法的输入数据，这三种方法就不再需要采用随机减量法或者自然激励技术法进行前处理，从而避免了这两种前处理方法的不准确性带来的误差。对两跨三层框架模型及一自锚式悬索桥模型的模态参数进行了识别，结果表明：基于协方差驱动SSI与数据驱动SSI的改进方法对比对应随机子空间法，在精度未减小的前提下提高了计算效率，仅用较少的数据就可较准确地识别出系统的模态参数，且识别精度较高、抗噪性较好；改进方法与ITD、STD、复指数法相比有精度上的优势。
③开展了在环境激励下的框架结构模态辨识实验，同时针对十二层钢筋混凝土框架结构的振动台试验模型进行了模态参数识别。结果进一步证明了所提出的改进方法的正确性、可行性；基于SSI法的改进辨识方法计算时间约为SSI法计算时间的50%，当输出信号较多时，这种优势更明显。从而可见，基于SSI法对ITD、STD、复指数法进行改进后，精度没有降低，同时缩短了计算时间，这将为改进方法应用到结构的实时监测提供了可能。
④在随机子空间辨识法与特征系统实现算法（ERA）的识别结构参数过程中，确定系统阶次是关键。研究了基于奇异值差分谱的去噪原理以及基于奇异值差分谱的分量分离原理。提出了基于奇异值差分谱的随机子空间和ERA模型定阶方法，通过该法来确定模型阶次所产生的虚假模态是最少的，且包含信号中所有模态，同时识别精度不受影响，并且计算量最小的阶次。通过试验和数值分析进行结构的模态识别，结果表明该方法是有效的。
⑤采用相关系数法进行真实模态分量的挑选，剔除低频虚假模态分量。采用数字滤波器对EMD分解进行改进，从而克服EMD分解时出现模态混叠的情况。针对经过EMD分解或者数字滤波后的单频率分量的信号，提出了基于奇异值差分谱的去噪的方法，仿真信号和实验数据分析表明该法去噪效果相当明显。提出了基于奇异值差分谱的模态分离HHT法，通过对仿真信号和实验数据的模态辨识，表明该方法是可行的。
⑥提出了基于数字滤波器的STD法、复指数法、ARMA法等三种识别方法，通过仿真信号、实验数据处理证明了方法的正确性、可行性，同时表明该方法能够有效分离密集模态，且在识别过程中无需考虑定阶问题。提出了基于EMD分解的STD法、复指数法、ARMA法等三种识别方法，通过仿真信号、实验数据证明了其正确性、可行性，同时表明该法能够处理非平稳信号，在识别过程中无需考虑定阶问题。
⑦在现有的直接解析法基础上，本文从三个方面对其进行了改进（包括直接解析法的模型缩聚改进，方程迭代解法的改进，模态截尾误差的改进），提出了框架结构损伤识别的改进直接解析法。针对五层两跨的框架结构，开展了基于改进模态参数灵敏度法的结构损伤识别方法研究，结果表明：在无噪声情况下识别结果非常正确，而在有噪声的情况下识别结果受到显著的影响，但在0.1%的噪声水平下，对于可接受识别结果的正确保证率可以达到80%以上。成果可为确立工程结构的科学鉴定系统，制定新的检测规范提供参考。
Modal parameter identification and damage identification technology ofengineering structures as a new subject to adapt to the actual needs of the project hasdeveloped for nearly20years, it has strong engineering background, also has importantpractical value. In recent years, the health monitoring and damage assessment ofengineering structure causes more and more attentions, modal parameter identificationand damage identification as its core technology and theoretical basis have becomeresearch hot spot in civil engineering field. It is too difficult to exert artificial excitationand efficiently measure excitation signal on engineering structures for their hugevolume, complex bind condition, mixed material, etc. Therefore traditional modalparameter identification theories and methods with testing input and output signal aredifficult to apply on engineering structures. Modal parameter identification underambient excitation have been widely used in the engineering field without applyingartificial incentives, without affecting the normal working, without measuring theexcitation signal, with low-cost and more in line with the actual situation, etc. theexisting modal parameter identification and damage identification methods have manydeficiencies in accuracy, robustness, efficiency and economic performance indicators,so they are still in the development stage, still need further study and perfect.
To provide new technology and tools with scientific, quantitative, non-destructive,real-time for the existing engineering structure detection, identification and evaluation,in this paper we carry out deeply research for modal parameter identification methodsunder ambient excitation and damage identification method based on modal parametersensitivity, to sum up the main content as follow:
①Through numerical analysis on a three layers framework model, we gotdisplacement response under ambient excitation, the two data pretreatment methods(random decrement technique and Next method) and five time domain modal parameteridentification method (ITD method, STD method, complex exponential method, ERAmethod and ARMA method) was selected to identify the modal parameters of thestructure, the results show: In the pretreatment methods Next method is superior torandom decrement technique method in terms of accuracy, anti-noise; STD method andARMA method are slightly higher than the other three methods in terms ofidentification accuracy, and STD method, ERA method ARMA method are slightly stronger than the other two methods in terms of anti-noise; frequency identificationaccuracy are much better than the damping identification accuracy in all methods.
②Combined with the stochastic subspace method, we proposed three improvedmodal parameter identification methods under ambient excitation (improved ITDmethod, improved STD method, improved complex exponential method). Stochasticsubspace method has high identification accuracy, covariance of data can retain all theuseful information in the original data, simultaneously remove noise. The data inToeplitz matrix as input for the ITD method, STD method and complex index method,these three methods will no longer need random decrement technique or Next methodfor pre-processing, thereby eliminating the error caused by these two pretreatmentmethods. By identifying the modal parameters of a two spans three layers frameworkand a self-anchored suspension bridge, we could get the results: comparing thecorresponding stochastic subspace method, the accuracy of the improved methods basedon the covariance-driven SSI and data-driven SSI is not reduced, but have highercomputationally efficient, they only use less data can accurately identify the modalparameters of the system, and the recognition accuracy is high, noise resistance is better;comparing the ITD, STD, complex exponential method, the improving methods havethe advantage on the accuracy.
③Modal identification experiments under ambient excitation on a frame structure,and modal parameter identification for the12-story reinforced concrete model shakingtable test were carried out in this paper. The recognition result further proved thecorrectness and feasibility of the proposed improved methods. In terms of accuracy ofthe five identification methods in the second chapter, ERA method is best, STD method,the complex exponential method and ARMA method closely followed, ITD method isthe worst. All methods can identify structural modal parameters under vibration effect.
④In this paper, we researched denoising principle and component separationprinciple that based on singular value differential spectrum. The determination of modelorder method was proposed based on singular value differential spectrum for stochasticsubspace and ERA method. The model order by this method generats least false modal,and containes all useful modal, at the same time the recognition accuracy is not affectedand needs the smallest amount calculation. Through numerical analysis for theexperimental data, the modal identification results show that the method is effective.
⑤To select real modal component and eliminate low frequency false modalcomponent, we applied correlation coefficient method. A digital filter to improve EMD decomposition was used, thereby overcoming the mode mixing phenomenon in EMDdecomposition. We proposed a denoising method based on singular value differentialspectrum for single-frequency components through EMD decomposition or digitalfiltering, simulated signals and experimental data analysis show that denoising effect ofthe method is quite obvious. We proposed a modal separation HHT method based onsingular value differential spectrum, through modal identification for simulated signalsand experimental data, it is proved that the method is feasible, also further broaden thehorizons for modal parameter identification under ambient excitation.
⑥Improved three identification methods(STD method, complex exponentialmethod, ARMA method) were presented based on the digital filter, the analysis forsimulated signals and experimental data proved the correctness and feasibility of theimproved method, at the same time show that this method can effectively separate theintensive modal and without regard the problem that how to determine modal order inthe recognition process. We improved three identification methods (STD method,complex exponential method, ARMA method) based on EMD decomposition, theanalysis for simulated signals and experimental data proved the correctness andfeasibility of the improved method, at the same time show that this method caneffectively handle non-stationary signals and without regard the problem that how todetermine modal order.
⑦Damage identification study based on improved modal parameter sensitivitymethod for a five-story frame structure has been done in this paper, we probed improveddirect analytical method for framework structural damage identification. Threeimprovements (including direct analytical method based on model reduction, theimprovement of modal truncation error, the improvement of the iterative solution of theequation) mainly be done. The numerical simulation analysis for the frame structureshow that: the recognition results is extremely correct in the case of noise-free, theresults suffer significant affect in the case of noise, but at the noise level of0.1%, for anacceptable recognition results guaranteed rate can reach80%or more. The research isuseful for scientific identification system in engineering structures, the developmentprovide a reference for the new test specifications.
针对目前研究中存在的问题，本文围绕环境激励下工程结构模态参数辨识方法和基于模态参数灵敏度的损伤识别方法开展研究，归结起来主要内容如下：
①计算三层钢筋砼框架模型在环境激励下的位移响应，利用两种数据预处理方法（随机减量法和NExT法）和ITD法、STD法、复指数法、ERA法和ARMA法等5种时域模态参数识别方法，开展了结构模态参数辨识的比较研究。结果表明：预处理方法中的NExT法在精度、抗噪性上均优于随机减量法；五种模态参数识别方法中STD法和ARMA法的对频率识别精度比其它三种方法稍高，在抗噪方面，STD、ERA法、ARMA法的抗噪能力比其它两种方法稍强，所有方法对频率的识别精度均远大于对阻尼比的识别精度。
②结合随机子空间法提出了环境激励下结构模态参数识别的改进ITD法、改进STD法与改进复指数法。随机子空间法的识别精度高，其中数据的协方差计算（矩阵正交投影计算）可以保留原始数据中的所有信息，同时去除了噪声，将得到的Toeplitz矩阵（P矩阵）中的数据作为ITD法、STD法与复指数法的输入数据，这三种方法就不再需要采用随机减量法或者自然激励技术法进行前处理，从而避免了这两种前处理方法的不准确性带来的误差。对两跨三层框架模型及一自锚式悬索桥模型的模态参数进行了识别，结果表明：基于协方差驱动SSI与数据驱动SSI的改进方法对比对应随机子空间法，在精度未减小的前提下提高了计算效率，仅用较少的数据就可较准确地识别出系统的模态参数，且识别精度较高、抗噪性较好；改进方法与ITD、STD、复指数法相比有精度上的优势。
③开展了在环境激励下的框架结构模态辨识实验，同时针对十二层钢筋混凝土框架结构的振动台试验模型进行了模态参数识别。结果进一步证明了所提出的改进方法的正确性、可行性；基于SSI法的改进辨识方法计算时间约为SSI法计算时间的50%，当输出信号较多时，这种优势更明显。从而可见，基于SSI法对ITD、STD、复指数法进行改进后，精度没有降低，同时缩短了计算时间，这将为改进方法应用到结构的实时监测提供了可能。
④在随机子空间辨识法与特征系统实现算法（ERA）的识别结构参数过程中，确定系统阶次是关键。研究了基于奇异值差分谱的去噪原理以及基于奇异值差分谱的分量分离原理。提出了基于奇异值差分谱的随机子空间和ERA模型定阶方法，通过该法来确定模型阶次所产生的虚假模态是最少的，且包含信号中所有模态，同时识别精度不受影响，并且计算量最小的阶次。通过试验和数值分析进行结构的模态识别，结果表明该方法是有效的。
⑤采用相关系数法进行真实模态分量的挑选，剔除低频虚假模态分量。采用数字滤波器对EMD分解进行改进，从而克服EMD分解时出现模态混叠的情况。针对经过EMD分解或者数字滤波后的单频率分量的信号，提出了基于奇异值差分谱的去噪的方法，仿真信号和实验数据分析表明该法去噪效果相当明显。提出了基于奇异值差分谱的模态分离HHT法，通过对仿真信号和实验数据的模态辨识，表明该方法是可行的。
⑥提出了基于数字滤波器的STD法、复指数法、ARMA法等三种识别方法，通过仿真信号、实验数据处理证明了方法的正确性、可行性，同时表明该方法能够有效分离密集模态，且在识别过程中无需考虑定阶问题。提出了基于EMD分解的STD法、复指数法、ARMA法等三种识别方法，通过仿真信号、实验数据证明了其正确性、可行性，同时表明该法能够处理非平稳信号，在识别过程中无需考虑定阶问题。
⑦在现有的直接解析法基础上，本文从三个方面对其进行了改进（包括直接解析法的模型缩聚改进，方程迭代解法的改进，模态截尾误差的改进），提出了框架结构损伤识别的改进直接解析法。针对五层两跨的框架结构，开展了基于改进模态参数灵敏度法的结构损伤识别方法研究，结果表明：在无噪声情况下识别结果非常正确，而在有噪声的情况下识别结果受到显著的影响，但在0.1%的噪声水平下，对于可接受识别结果的正确保证率可以达到80%以上。成果可为确立工程结构的科学鉴定系统，制定新的检测规范提供参考。
Modal parameter identification and damage identification technology ofengineering structures as a new subject to adapt to the actual needs of the project hasdeveloped for nearly20years, it has strong engineering background, also has importantpractical value. In recent years, the health monitoring and damage assessment ofengineering structure causes more and more attentions, modal parameter identificationand damage identification as its core technology and theoretical basis have becomeresearch hot spot in civil engineering field. It is too difficult to exert artificial excitationand efficiently measure excitation signal on engineering structures for their hugevolume, complex bind condition, mixed material, etc. Therefore traditional modalparameter identification theories and methods with testing input and output signal aredifficult to apply on engineering structures. Modal parameter identification underambient excitation have been widely used in the engineering field without applyingartificial incentives, without affecting the normal working, without measuring theexcitation signal, with low-cost and more in line with the actual situation, etc. theexisting modal parameter identification and damage identification methods have manydeficiencies in accuracy, robustness, efficiency and economic performance indicators,so they are still in the development stage, still need further study and perfect.
To provide new technology and tools with scientific, quantitative, non-destructive,real-time for the existing engineering structure detection, identification and evaluation,in this paper we carry out deeply research for modal parameter identification methodsunder ambient excitation and damage identification method based on modal parametersensitivity, to sum up the main content as follow:
①Through numerical analysis on a three layers framework model, we gotdisplacement response under ambient excitation, the two data pretreatment methods(random decrement technique and Next method) and five time domain modal parameteridentification method (ITD method, STD method, complex exponential method, ERAmethod and ARMA method) was selected to identify the modal parameters of thestructure, the results show: In the pretreatment methods Next method is superior torandom decrement technique method in terms of accuracy, anti-noise; STD method andARMA method are slightly higher than the other three methods in terms ofidentification accuracy, and STD method, ERA method ARMA method are slightly stronger than the other two methods in terms of anti-noise; frequency identificationaccuracy are much better than the damping identification accuracy in all methods.
②Combined with the stochastic subspace method, we proposed three improvedmodal parameter identification methods under ambient excitation (improved ITDmethod, improved STD method, improved complex exponential method). Stochasticsubspace method has high identification accuracy, covariance of data can retain all theuseful information in the original data, simultaneously remove noise. The data inToeplitz matrix as input for the ITD method, STD method and complex index method,these three methods will no longer need random decrement technique or Next methodfor pre-processing, thereby eliminating the error caused by these two pretreatmentmethods. By identifying the modal parameters of a two spans three layers frameworkand a self-anchored suspension bridge, we could get the results: comparing thecorresponding stochastic subspace method, the accuracy of the improved methods basedon the covariance-driven SSI and data-driven SSI is not reduced, but have highercomputationally efficient, they only use less data can accurately identify the modalparameters of the system, and the recognition accuracy is high, noise resistance is better;comparing the ITD, STD, complex exponential method, the improving methods havethe advantage on the accuracy.
③Modal identification experiments under ambient excitation on a frame structure,and modal parameter identification for the12-story reinforced concrete model shakingtable test were carried out in this paper. The recognition result further proved thecorrectness and feasibility of the proposed improved methods. In terms of accuracy ofthe five identification methods in the second chapter, ERA method is best, STD method,the complex exponential method and ARMA method closely followed, ITD method isthe worst. All methods can identify structural modal parameters under vibration effect.
④In this paper, we researched denoising principle and component separationprinciple that based on singular value differential spectrum. The determination of modelorder method was proposed based on singular value differential spectrum for stochasticsubspace and ERA method. The model order by this method generats least false modal,and containes all useful modal, at the same time the recognition accuracy is not affectedand needs the smallest amount calculation. Through numerical analysis for theexperimental data, the modal identification results show that the method is effective.
⑤To select real modal component and eliminate low frequency false modalcomponent, we applied correlation coefficient method. A digital filter to improve EMD decomposition was used, thereby overcoming the mode mixing phenomenon in EMDdecomposition. We proposed a denoising method based on singular value differentialspectrum for single-frequency components through EMD decomposition or digitalfiltering, simulated signals and experimental data analysis show that denoising effect ofthe method is quite obvious. We proposed a modal separation HHT method based onsingular value differential spectrum, through modal identification for simulated signalsand experimental data, it is proved that the method is feasible, also further broaden thehorizons for modal parameter identification under ambient excitation.
⑥Improved three identification methods(STD method, complex exponentialmethod, ARMA method) were presented based on the digital filter, the analysis forsimulated signals and experimental data proved the correctness and feasibility of theimproved method, at the same time show that this method can effectively separate theintensive modal and without regard the problem that how to determine modal order inthe recognition process. We improved three identification methods (STD method,complex exponential method, ARMA method) based on EMD decomposition, theanalysis for simulated signals and experimental data proved the correctness andfeasibility of the improved method, at the same time show that this method caneffectively handle non-stationary signals and without regard the problem that how todetermine modal order.
⑦Damage identification study based on improved modal parameter sensitivitymethod for a five-story frame structure has been done in this paper, we probed improveddirect analytical method for framework structural damage identification. Threeimprovements (including direct analytical method based on model reduction, theimprovement of modal truncation error, the improvement of the iterative solution of theequation) mainly be done. The numerical simulation analysis for the frame structureshow that: the recognition results is extremely correct in the case of noise-free, theresults suffer significant affect in the case of noise, but at the noise level of0.1%, for anacceptable recognition results guaranteed rate can reach80%or more. The research isuseful for scientific identification system in engineering structures, the developmentprovide a reference for the new test specifications.
引文
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