【作者】 张茂雨；

【导师】 薛松涛； 唐和生；

【作者基本信息】 同济大学 ， 结构工程， 2007， 博士

【摘要】 本文首先简述了当前结构损伤识别领域的研究状况和发展趋势，论述了支持向量机方法的基本原理与算法，并阐明了本文研究的课题背景和主要研究内容。本文立足于损伤模式识别与在线参数识别两方面问题，阐述了传统方法的缺陷，对其加以改进，提高识别精度、识别效率及其鲁棒性。模式识别是一种简单常用的离线损伤识别方法，但动力指纹采用恰当与否对识别结果有很大的影响。结构固有频率是最易提取且测量误差较小的动力指纹，但传统方法对结构固有频率不敏感，损伤程度不易识别；而其他动力指纹虽然具有较好的灵敏度，但实际测量误差大等原因限制了其应用。而支持向量机方法解决了传统模式识别方法对频率变化不敏感的缺陷，采用结构损伤前后的固有频率变化率为动力指纹，不仅能对损伤进行准确定位，而且能识别结构损伤的程度。在模式识别方法中，采用的核函数适当与否直接关系到动力指纹与损伤之间的影射关系，从而影响到识别效果。本文结合小波函数与高斯核函数提出了小波核函数，数值模拟的结果表明，采用小波核函数识别结构损伤有更好的识别效果，尤其是在多损伤情况下，识别精度显著优于其他常用的核函数。小波核函数支持向量机模式识别方法简单方便，而且对测量误差较小的频率变化率有较高的灵敏度，弥补了传统方法的局限性。对十层剪切型框架结构的数值模拟结果表明，该方法具有良好的识别精度，尤其是对单损伤情况下，不仅能准确定位，而且对损伤的程度有很高的识别精度。用单损伤训练的支持向量机同时也适用于多损伤情况，在多损伤情况下，能准确定位损伤的位置，损伤程度的识别结果稍有误差，但仍能得到令人满意的结果，而且有很好的抗噪声能力。在线识别技术能直接识别出结构的动力参数，更加符合实际工程的需求。最小二乘支持向量机(LS-SVM)是对传统在线参数识别方法的改进，通过使用等式约束和二次损失函数将标准SVM方法的二次规划问题求解转化成为线性方程组的求解，从而提高了支持向量机的训练速度。但是LS-SVM方法丧失了标准SVM方法的稀疏性，而且，当一个新数据输入时，需要重新求解整个线性方程组。LS-SVM方法仍然存在识别精度不高，识别效率低，鲁棒性差的缺陷，因此，本文在LS-SVM方法的基础上，提出了改进方法。首先是基于增量式LS-SVM回归方法提出了增量式加权特征向量LS-SVM回归方法，通过对特征向量的加权，区分各样本在识别中的贡献大小，从而提高了识别精度。但增量式算法将所有数据都纳入识别样本集，计算效率低，为了实现在线识别，需要更高的硬件要求。于是提出了等样本集LS-SVM递归算法，通过局部增加算法与修剪算法，及时更新样本，在加入新样本的同时，剔除过时样本，避免了多次的矩阵求逆运算，大大提高了计算效率，使在线识别成为可能。在等样本集LS-SVM递归算法基础上，提出了自适应误差加权方法与自适应特征向量指数加权方法，根据回归估计的误差大小赋予样本权重，更进一步提高了识别精度与鲁棒性。对不同的结构损伤模式、受不同噪声干扰的情况进行在线识别，结果表明加权后的等样本集LS-SVM回归方法有更高的识别精度和识别效率，并具有很好的抗噪性能，尤其是自适应特征向量指数加权方法。将前面的研究成果应用于实际工程。对一振动台试验模型的结构进行损伤识别，识别结果与试验现象基本吻合。最后对全文的主要工作和研究成果进行了总结，并指出有待进一步改进和研究的方向。更多还原

【Abstract】 In this dissertation, the state of arts of the researches about structural damageidentification is depicted, and the rationale of support vector machine and thearithmetic are also introduced. Then the background of the research project and thecontent of this dissertation are outlined. This dissertation focuses on patternrecognition and online parameter identification, and improves the traditional methodto increase the precision, efficiency and robustness of the identification.Pattern recognition is a simple and convenient method, but whether the dynamicfingerprint is right or not makes great effect on the results. The natural frequency isan easy obtained dynamic fingerprint, further more the measure error of it is least. Butthe traditional method is insensitive to the natural frequency, and it is difficult toidentify the degree of the damage. Other dynamic fingerprints are more sensitive todamage, but the great measure error limits their application. However, the supportvector machine method overcomes the drawback of the traditional method, which isinsensitivity to the natural frequency. It can not only recognize the location of damage,but also can identify the degree of damage.Kernel function is the key for the support vector machine in the patternrecognition. It reflects the relation between the dynamic fingerprint and damage, andaffects the result of identification. Combining the wavelet function and Goss Kernelfunction, the Wavelet Kernel function is presented. Numerical analysis shows that theWavelet Kernel function is evidently better than the others, especially for the case ofmultiple damages.The Wavelet Kernel function LS-SVM is an convenient method for patternrecognition, further more it is more sensitive to the change rate of natural frequencywhich has less measure error. This new method remedies the shortages of traditionalmethod. The result of numerical simulation about a 10-story frame shows that thismethod has a better precision. Especially under the condition of single damage, it cannot only recognize the location of damage correctly, but also has a high precision on the damage degree. The machine which trained by single damage is also suitable tothe multiple damage. Under the condition of multiple damage, although the result ofdamage degree identification has some errors, it also can get the satisfying result andhas better robustness as well.The technique of online identification can identify the structural dynamicparameters directly, which can fit the need of project better. Least Square SupportVector Machine (LS-SVM) is an improvement on traditional methods, which makesa great improvement on the training speed. But LS-SVM method loses the matrix’ssparseness of standard SVM method. Furthermore, it needs to re-resolve the wholelinear equation set when a new set of data is input. So the LS-SVM method still hassome shortages such as low identification precision, low identification efficiency, andweak robustness. Therefore, improved method based on LS-SVM is put forward inthis dissertation.At first, the incremental weighted eigenvector LS-SVM regression method basedon the incremental LS-SVM regression method is presented. This new methodimproved the identification precision via weighting the eigenvector anddistinguishing the contribution magnitude of every sample. But the incrementalalgorithm puts the whole data into the identification sample set, which makes thecomputing efficiency lower. It requires relatively higher hardware to implement theonline identification. Thus, the equal sample LS-SVM recursion algorithm ispresented, according to partial incremental algorithm and pruned algorithm to updatethe sample in time, when the new sample is input, the outdated sample is eliminatedat the same time. The repeating matrix inversions are avoided to greatly improve thecomputing efficiency. Consequently, the identification online becomes possible.On the base of the equal sample LS-SVM, the adaptive error weighted LS-SVMand the adaptive eigenvector exponential weighted LS-SVM are presented. These twonew methods put the eigenvector different weight according to the error. Thereby, theprecision and robustness are improved. Some numerical simulation examples,including different damage patterns and different forms of noise, are analyzed, whichindicate that the weighted equal sample LS-SVM methods are excellent methods foronline identification, which are more accurate and efficient, and have better robustness as well, especially for the adaptive eigenvector exponential weightedLS-SVM method.The methods introduced above are applied to an experimental structure which isa 12-story frame. The result of the damage identification is in accord with thephenomena of the experiment by and large.At last, the main contributions and conclusions of this dissertation aresummarized and some problems which need further research are set forward.更多还原