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题名	谐振频率对多层结构下背覆薄层厚度的反演检测
作者	周昌智
学位类别	博士
答辩日期	2008-06-02
授予单位	中国科学院声学研究所
授予地点	声学研究所
关键词	超声谱 无损评价 薄层 谐振频率 模拟退火
其他题名	Determination of thickness of a thin film under a multilayered media by resonant frequencies
学位专业	声学
中文摘要	本文首先简单介绍了用于薄层检测的几种常用方法，并着重介绍了其中的超声谱方法；针对不同的研究对象，超声谱方法的不同应用各有利弊。接着依据逆问题的最优化求解要求，介绍了常见的模拟退火方法系列，并进行了一定的比较。 对纵横波任意角度入射于由各向同性介质组成的多层结构的问题，引入矩阵方法推导出相应的系统反射系数，并针对实际研究对象给出了声波垂直入射于整个多层结构时系统的反射系数。反射系数幅度谱中，对应于局部极小值的频率点即为系统谐振频率。这些谐振频率是由多层结构系统的多模式耦合振动产生。以一个特定的“钢/环氧树脂/铝/聚合物”多层结构为例，分析表明系统的谐振频率仅与介质的渡越时间有关，而与介质的特性阻抗和等效衰减因子近乎无关。当多层结构中的背覆薄层厚度为唯一变量时，问题得到了进一步的简化。从谐振频率与背覆薄层厚度之间的变化关系中我们在一些特定的背覆薄层厚度区间内找到一些随厚度敏感的谐振频率。通过对这些区域内谐振频率的敏感性分析，我们分别定义那些具有较大敏感函数值和较小敏感函数值的谐振频率为“敏感谐振频率”和“非敏感谐振频率”，而将该厚度范围内所对应的包含有敏感谐振频率的区域称为“敏感谐振频率窗”。从多层结构中位移分布的角度出发，计算得到的敏感谐振频率下背覆薄层中声波的位移振幅要远大于非敏感谐振频率时情形；从多层结构中应变能角度分析，敏感谐振频率时背覆薄层中的应变能比要远大于非敏感谐振频率时的情形，其中“应变能比”定义为某一谐振模式下某一介质中的应变能占整个系统应变能的比例。从这两个角度出发，我们得到了多层结构系统中的振动情况并较好地解释了敏感谐振频率的成因。 对一个实际的“钢/环氧树脂/铝/聚合物”多层结构样品，实验测量了其在2 MHz-8MHz范围内的谐振频率点，实验结果与理论计算基本吻合，所有谐振频率点的误差均小于2.5%，这些谐振频率均位于相应的“敏感谐振频率窗”内。在敏感谐振频率随厚度敏感变化的分析基础上，我们确定了逆问题的目标函数：当目标函数取全局最小值时，背覆薄层厚度的理论假设值与真实值一致。当多层结构中不存在噪声且参数无误差时，数值计算的结果表明快速模拟退火方法用于厚度反演问题时具有较高的精度；当系统参数中加入±1% 误差和时域中混入5%高斯白噪声时，计算结果说明引入的非常快速模拟退火算法适用于一定误差范围内的从谐振频率中获得背覆薄层厚度的反演问题。将实验中测量得到的多个谐振频率点代入目标函数后，采用非常快速模拟退火方法反演，得到的背覆薄层厚度与其直接测量值之间吻合得较好。针对我们的实验对象，分别采用等效近似厚度（或声速）的方法以及二次降温的变目标函数模拟退火方法分别对反演结果进行改进，得到了一定条件下背覆薄层厚度反演结果的改善。相应的计算结果也表明，这种方法不仅适用于背覆薄层厚度的反演，也可用于多层结构中任意一层介质厚度的反演，还可以用于整个系统所有层厚度的反演。当其他参量已知的时候，这一方法也可用于多层结构中任一层或所有层介质纵波声速的反演。这一方法的本质在于从介质中声波传播时间相关的多个谐振频率点中反演出各层的渡越时间。本文中，当入射声波频率为6MHz时，背覆薄层的厚度与其中沿厚度方向的声波波长比最小约为1/5，而环氧树脂粘接层中的厚度-波长比则约为1/25。 本文的主要贡献和创新点包括：1. 采用垂直入射的声波对多层结构下的薄层进行评价，谐振频率仅与背覆薄层渡越时间有关；2. 从反射系数以及谐振频率的计算中找到一定背覆薄层厚度范围内与背覆薄层厚度敏感的敏感谐振频率和相应的敏感谐振频率窗作为逆问题运算的基础；3. 定义参量应变能比用以敏感谐振频率的物理解释；4. 将非常快速模拟退火算法用于逆问题，利用敏感谐振频率的特性成功地完成背覆薄层厚度以及所有层厚度的反演。
英文摘要	By introducing several QNDE (Quantitative Nondestructive Evaluation) methods for characterization of thin layers, the ultrasonic spectroscopy method is highlighted here. For different situations of evaluation of thin layers, the corresponding ultrasonic spectroscopy methods have been developed with their special advantages and shortages. For the optimization of the inverse problem, the Simulated Annealing(SA) method serials are presented and compared. The reflection coefficient of a multilayered system consisting of isotropic and homogeneous parallel layers is deduced by the transfer matrix method. Specifically, when the normal incident longitudinal wave is transmitted upon the n-layer media, the reflection coefficient can be written in the term of the reflection coefficient of the (n-1)-layer media. The resonant frequencies of the multilayered media are given by searching the minima in the amplitude spectra of the reflection coefficient. The essential of these resonant frequencies are the complex compound vibration in the lamination system. For a concrete multilayered system like “steel/epoxy resin/aluminum/thin polymer”, the relationship between the resonant frequencies and the three acoustical parameters of the thin film are plotted. The result reveals that the resonant frequencies are sensitive to the time-of-flight in the thin film, but keeps nearly still when the characteristic acoustic impedance and normalized attenuation of the thin film change. By assuming the thickness of the thin film be the only variable in the whole problem, the relationship between the resonant frequencies and the thickness of the thin film has been detailed: in certain range of the thin film layer thickness, some of the resonant frequencies shift dramatically when the thickness changes, while the others seem to be unrelated with the thickness changing. From the result of the sensitivity analysis of the resonant frequencies to the thin film thickness, we call those resonant frequencies with high sensitivity values the “sensitive resonant frequencies”, while the others are the “non-sensitive resonant frequencies”. The region in the certain range of the thin film thickness containing the sensitive resonant frequencies is named as the “sensitive resonant frequencies region”. The displacement in the multilayered system shows the vibration characters of the system in different resonant modes. For the resonant modes of the sensitive resonant frequency, the amplitudes of displacement in the thin film are much larger than the others. We try to explain this phenomenon from the aspect of strain energy in the system by defining the parameter of strain energy ratio, which indicates how much the strain energy in a layer takes up in the total strain energy in the whole system under a resonant mode. For the resonant modes of the sensitive resonant frequency, the strain energy ration in the thin film layer is extra higher than the values under the other modes. And this gives a reliable physical interpretation of the sensitive natural frequencies. Experiment has been carried out on a “steel/epoxy resin/aluminum/thin polymer” structured specimen. The results in 2MHz-8MHz show good agreements with the theoretical ones: the relative error of all these resonant frequencies are less than 2.5%, and all of the sensitive resonant frequencies are located in the sensitive resonant frequencies region, as predicted. With the sensitivity analysis of different resonant frequencies, the objective function is established for the inverse problem based on the well-known least-squares sense: when the objective function drops into a global minimum, the corresponding thickness is considered as the real value of the thin layer. The simulated annealing (SA) method is employed and verified by several numerical simulation calculations. By the resonant frequencies from an ideal system with no measure error and signal noise, the results show that, the SA method has a quite high precision for the inverse problem of the thin film; By the resonant frequencies from a system with ±1% measurement error and 5% Gaussian white noise of signal in the time domain, the results indicate that, this method is good enough for this level of measurement error and noise; By the resonant frequencies from the measured signal, the results show good agreements with the real values. Some remarkable improvements of inversion of the thin layer thickness have been progressed in this problem: approximate parameter of thicknesses or longitudinal wave velocities for cancellation of various errors in the system; re-annealing with different objective function in the SA method for the arbitral role of the sensitive resonant frequencies. Actually, this method can not only be applied in the inverse problem of the thin layer thickness under the multilayered media, but also be expanded to determinate any layer thickness of the lamination, even all of the layer thicknesses. This method is still available for the inversion of the longitudinal wave velocity of any layer by given the other parameters. The soul of this solution is the capability of inversion of the time-of-flight in every layer from the resonant frequencies which is a correlative parameter of wave propagation time in the multilayered media. When the frequency of the wave is 6MHz, the thickness to wavelength ratios (h/λ) in the thin film and the adhesive joint are about 1/5 and 1/25, respectively. The main contributions and innovative works of the dissertation include: 1. Only the normal incident wave is applied for characterization of a thin film underneath a multilayered system of different materials, and the resonant frequencies are only sensitive to the time-of-flight of the undermost thin layer; 2. The sensitive resonant frequencies and the sensitive resonant frequencies region are found from the relationship between the numerically calculated resonant frequencies and the thickness of the undermost thin layer; 3. The strain energy ratio is defined and presented for a physical interpretation of the sensitive natural frequency; 4. By employing the Very Fast Simulated re-Annealing method, the thickness of the undermost thin layer and all the thicknesses of the multilayer system are inversed successfully from the resonant frequencies including the sensitive ones.
语种	中文
公开日期	2011-05-07
页码	87
内容类型	学位论文
源URL	[http://159.226.59.140/handle/311008/272]
专题	声学研究所_声学所博硕士学位论文_1981-2009博硕士学位论文
推荐引用方式 GB/T 7714	周昌智. 谐振频率对多层结构下背覆薄层厚度的反演检测[D]. 声学研究所. 中国科学院声学研究所. 2008.

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