论文标题:结构分析中的多输入多输出传递函数无偏估计
论文作者
论文导师 吴运新,论文学位 硕士,论文专业 机械设计及理论
论文单位 中南大学,点击次数 86,论文页数 88页File Size2466k
论文网 http://www.lw23.com/lunwen_1006535002/
Experimental modal analysis;Frequency;response;function;estimator;digital signal process
实验模态分析是基于实测数据建立系统数学模型的技术。随着电子技术与计算机技术的发展,实验模态分析已经成为解决复杂结构振动问题的主要工具。传递函数是联系实测数据和模态参数识别的中间环节,是模态参数识别的基础,传递函数估计的精度决定了模态参数识别的精度。 当前所广泛使用的传递函数估计方法是H_1估计和H_2估计,这两种估计方法均为有偏估计方法,而近期提出的几种无偏估计方法又存在着不易实现的问题。针对这种情况,本文对现有的传递函数估计方法进行了分析研究,指出互功率谱技术和平均技术是估计得到无偏的、高精度的传递函数的关键。在此分析的基础上,本文提出了一种互功率谱传递函数估计方法--H_n估计;与不同的激励方法相结合,得到了单点激励H_n估计、多点随机激励H_n估计和多点全相干H_n估计;对弹簧、质量、阻尼结构的物理模型,编程实现了单输入单输出(SISO)H_n估计和多点全相干H_n估计及其和H_1估计结果的比较;以两端铰支梁为实验对象做了单输入单输出实验,利用自己编制的程序实现了传递函数的H_n估计和H_1估计及H_2估计的比较。理论推导和实验表明,H_n估计是一种无偏的、高精度的传递函数估计方法。该方法充分利用了互功率谱技术和平均技术,在不需要测试第三种信号的情况下,实现了传递函数的无偏估计;在测量同样组数据的情况下,能够进行更多次数的平均,从而提高了传递函数的估计精度。
Experimental modal analysis is a technique to build modal model based on the measured data. With the development of the electronic technique and the computer technology, experimental modal analysis has been the main tool to solve complex structure"s vibration problems. Frequency Response Function (FRF) is a ring that links the measured data and the modal parameter recognition (MPR). It is the foundation of the modal parameter recognition. The precision of the frequency response function estimation decides the precision of the MPR.Presently, because the existing several unbiased Frequency Response Function estimators are difficult to realize, the most popular and widely-spread used Frequency Response Function estimators are H_1, and H_2, although both of them are biased ones. In allusion to such situation, some typical Frequency Response Function estimators are analyzed. It is pointed that the cross spectrum density technique and the meaning technique is the key technique to get the unbiased and high precision FRF. On the basis of such analysis, a completed cross spectrum density frequency response function estimator- H_n estimator isproduced. Through the combination of the H_n with different excitation methods, single-input single-output and multi-point random and multi-point mono-phased harmonic H_n estimators are deduced. For a multi-degree-of-freedom viscous damping system, simulation analysis is made to realize the single-input single-output and the multi-point mono-phased harmonic H_n estimators and the comparison with the H_1 estimator. For a both end hinged beam, experiment is made which realized the comparison of H_n and H_1 and H_2. Through the simulation analysis and the experiment, it is proved that H_nis an unbiased and high precision estimator. This method makes the best of the cross spectrum density technique and the meaning technique. It realized the unbiased frequency response function estimator need not to measure the third signal. With the same number of measured data, it can mean more times, which improved the precision of the frequency response function estimation.
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