Damage identification for beams in noisy conditions based on Teager energy operator-wavelet transform modal curvature

Modal curvatures have been widely used in the detection of structural damage. Attractive features of modal curvature include great sensitivity to damage and instant determination of damage location. However, an intrinsic deficiency in a modal curvature is its susceptibility to the measurement noise present in the displacement mode shape that produces the modal curvature, likely obscuring the features of damage. To address this deficiency, the Teager energy operator together with wavelet transform is tactically utilized to treat modal curvature, producing a new modal curvature, termed the Teager energy operator-wavelet transform modal curvature. This new modal curvature features distinct capabilities of suppressing noise, canceling global trends, and intensifying the singular feature caused by damage for a measured mode shape involving noise. These features maximize the sensitivity to damage and accuracy of damage localization. The proposed modal curvature is demonstrated in several analytical cases of cracked pinned–pinned, clamped–free and clamped–clamped beams, with emphasis on characterizing damage in noisy conditions, and it is further validated by an experimental program using a scanning laser vibrometer to acquire mode shapes of a cracked aluminum beam. The Teager energy operator-wavelet transform modal curvature essentially overcomes the deficiency of conventional modal curvature, providing a new dynamic feature well suited for damage characterization in noisy environments. (The Matlab code for implementing Teager energy operator-wavelet transform modal curvature can be provided by the corresponding author on request.)     

STRUCTURAL DAMAGE DETECTION BASED ON A MICRO-GENETIC ALGORITHM USING INCOMPLETE AND NOISY MODAL TEST DATA

This paper describes a procedure for detecting structural damage based on a micro-genetic algorithm using incomplete and noisy modal test data. As the number of sensors used to measure modal data is normally small when compared with the degrees of freedom of the finite element model of the structure, the incomplete mode shape data are first expanded to match with all degrees of freedom of the finite element model under consideration. The elemental energy quotient difference is then employed to locate the damage domain approximately. Finally, a micro-genetic algorithm is used to quantify the damage extent by minimizing the errors between the measured data and numerical results. The process may be either of single-level or implemented through two-level search strategies. The study has covered the use of frequencies only and the combined use of both frequencies and mode shapes. The proposed method is applied to a single-span simply supported beam and a three-span continuous beam with multiple damage locations. In the study, the modal test data are simulated numerically using the finite element method. The measurement errors of modal data are simulated by superimposing random noise with appropriate magnitudes. The effectiveness of using frequencies and both frequencies and mode shapes as the data for quantification of damage extent are examined. The effects of incomplete and noisy modal test data on the accuracy of damage detection are also discussed.     

Decentralized detection for B5G massive MIMO: When local computation meets iterative algorithm

Massive multiple-input multiple-output (MIMO) is a key enabler for 5G and beyond. For signal detection of massive MIMO, computing resources available at the network edge were underexplored in most existing algorithms. For this reason, the paper proposes a new detection algorithm, termed inner-looping decentralized generalized expectation consistent for signal recovery (iDeGEC-SR), which leverages an extra (inner) loop of message passing added to the DeGEC-SR and makes better exploration of the local computing resources. As demonstrated by theoretical analysis and Monte Carlo simulations, the algorithm outperforms state-of-the-art techniques like GEC-SR (in terms of computational complexity), GAMP and DeGEC-SR (in terms of estimation accuracy), considerably.     

峰值能量检测及其在被动声纳显示中的应用

本文介绍子带峰值能量检测方法及其在被动声纳显示和检测中的应用[2-4]，同时提出了波束域宽带峰值能量检测算法。新的波束域算法是在已有波束形成的基础上进行处理，不需对原系统进行较大的修改。通过波束域宽带峰值能量检测处理，可以改善声纳显示效果，更加清晰地显示目标方位。相对于高分辨率波束形成算法，两种峰值能量检测算法的运算量都比较低，具有一定的工程应用前景。通过计算机仿真和实测数据处理，验证了所述两种峰值能量算法在提高显示清晰度，减小测向模糊度方面的优点。     

Statistical damage identification of structures with frequency changes

Model updating methods based on structural vibration data have being rapidly developed and applied to detect structural damage in civil engineering. But uncertainties existing in the structural model and measured vibration data might lead to unreliable damage detection. In this paper a statistical damage identification algorithm based on frequency changes is developed to account for the effects of random noise in both the vibration data and finite element model. The structural stiffness parameters in the intact state and damaged state are, respectively, derived with a two-stage model updating process. The statistics of the parameters are estimated by the perturbation method and verified by Monte Carlo technique. The probability of damage existence is then estimated based on the probability density functions of the parameters in the two states. A higher probability statistically implies a more likelihood of damage occurrence. The presented technique is applied to detect damages in a numerical cantilever beam and a laboratory tested steel cantilever plate. The effects of using different number of modal frequencies, noise level and damage level on damage identification results are also discussed.     

一种改进的稀疏近似最小方差DOA估计算法研究

针对稀疏信号的超分辨方位估计问题,提出一种可变因子的稀疏近似最小方差算法(α-Sparse Asymptotic Minimum Variance,简记为SAMV-α)。该算法利用一个折衷参数进行最大似然估计值和稀疏性能的折衷处理,在迭代过程中改变稀疏近似最小方差算法(Sparse Asymptotic Minimum Variance,SAMV)的指数因子,得到强稀疏性能和超低旁瓣的方位谱图,实现邻近目标的超分辨方位估计和相干处理性能,且无需预估角度和信源数目等先验信息,并且折衷参数的取值为0到1之间,取值区间明确,避免了稀疏信号处理算法中正则因子选取困难的弊端。计算机仿真表明SAMV-α算法方位估计性能明显优于波束扫描类算法和子空间类算法,与同类型稀疏信号处理类算法相比仍具有较高的方位估计精度,同时对于邻近声源分辨能力,SAMV-α算法较SAMV-1算法性能提高约3dB。海上试验数据处理给出了分辨率更高的方位时间历程(Bering-Time Recording,BTR)图,有效验证了SAMV-α算法的性能。      

Computing communities in complex networks using the Dirichlet processing Gaussian mixture model with spectral clustering

Community detection becomes a significant tool for the complex network analysis. The study of the community detection algorithms has received an enormous amount of attention. It is still an open question whether a highly accurate and efficient algorithm is found in most data sets. We propose the Dirichlet Processing Gaussian Mixture Model with Spectral Clustering algorithm for detecting the community structures. The combination of traditional spectral algorithm and new non-parametric Bayesian model provides high accuracy and quality. We compare the proposed algorithm with other existing community detecting algorithms using different real-world data sets and computer-generated synthetic data sets. We show that the proposed algorithm results in high modularity, and better accuracy in a wide range of networks. We find that the proposed algorithm works best for the large size of the data sets.     

GUW-based structural damage detection using WPT statistical features and multiclass SVM

Recently, guided ultrasonic waves (GUW) are widely used for damage detection in structural health monitoring (SHM) of different engineering structures. In this study, an intelligent damage detection method is proposed to be used in SHM applications. At first, GUW signal is de-noised by discrete wavelet transform (DWT). After that, wavelet packet transform (WPT) is employed to decompose the de-noised signal and the statistical features of decomposed packets are extracted as damage-sensitive features. Finally, a multiclass support vector machine (SVM) classifier is used to detect the damage and estimate its severity. The proposed method is employed for GUW-based structural damage detection of a thick steel beam. The effects of different parameters on the sensitivity of the method are surveyed. Furthermore, by comparing with some other similar algorithms, the performance of the proposed method is verified. The experimental results demonstrate that the proposed method can appropriately detect a structural damage and estimate its severity.     

Automated data-based damage localization under ambient vibration using local modal filters and dynamic strain measurements: Experimental applications

This paper deals with the experimental application of modal filters for automated damage localization using dynamic strain measurements. Previously developed for damage detection, the extension of modal filtering to damage localization consists in splitting a very large network of dynamic strain sensors into several independent local sensor networks. An efficient signal processing coupled to control charts allows a fully automated data-based damage localization once the modal filters are initialized. The method is tested experimentally on a small clamped-free steel plate and a 3.78 m long steel I-beam, both instrumented with a network of cheap piezoelectric patches to measure the dynamic strains. A removable damage is introduced at different positions by means of a small removable damage device. For both applications, the method can successfully detect and locate all damage cases considered, showing the potentiality of the method for field applications.     

基于最小Csiszár’s I-散度的高精度深度定位方法*

模态波束形成技术可用于水下目标定位,在深度定位方面,其定位精度(百米量级)往往不能满足实际需求;因此,高精度的深度定位方法需要被探索。传统高精度估计方法,如最小方差无畸变响应,面临着许多问题,如需要大量的快拍样本数等。最小Csiszár’s I-散度的迭代算法可以解决线性系统的求逆问题,但需满足系统的非负性条件,在图像的去模糊领域已得到广泛应用。该文将此算法和模态波束形成技术相结合,提出了一种新的高精度深度定位方法。基于SWellEx-96实验的海洋环境参数,分别用仿真和实验数据验证了该方法的以下性能：实现深度的高精度定位且抑制旁瓣能量;在小快拍数的情况下,深度定位性能良好。     

一种基于模态域波束形成的水平阵被动目标深度估计

水面水下目标分辨与识别一直是被动声呐探测领域的难题.利用一种水平阵模态域波束形成算法获得己知方位目标声源的各阶模态强度,将其与不同深度的各阶参考模态强度进行匹配,最终实现了对声源的深度估计.仿真结果表明,该算法可以在信噪比为-10 dB的情况下,用300Hz带宽的信号样本,实现对声源深度的有效估计.系统分析了不同参数和不同波导条件对该方法目标深度估计性能的影响.其中,阵元数越多,模态样本数越多,计算频段越宽,方位估计精度越高,有效阵长越长,深度估计的性能越好.阵元间距和波导深度的变化不会影响该方法的深度估计性能,并且该方法的深度估计性能在声速剖面、海底参数等波导条件存在扰动时具有鲁棒性.     

The dynamic analysis of a cracked Timoshenko beam by the spectral element method

The aim of this paper is to introduce a new finite spectral element of a cracked Timoshenko beam for modal and elastic wave propagation analysis. The proposed approach deals with the spectral element method. This method is suitable for analyzing wave propagation problems as well as for calculating modal parameters of the structure. In the paper, the results of the change in modal parameters due to crack appearance are presented. The influence of the crack parameters, especially of the changing location of the crack, on the wave propagation is examined. Responses obtained at different points of the beam are presented. Proper analysis of these responses allows one to indicate the crack location in a very precise way. This fact is very promising for the future work in the damage detection field.     

Condition assessment of reinforced concrete beams using dynamic data measured with distributed long-gage macro-strain sensors

A new condition assessment strategy of reinforced concrete (RC) beams is proposed in this paper. This strategy is based on frequency analysis of the dynamic data measured with distributed long-gage macro-stain sensors. After extracting modal macro-strain, the reference-based damage index is theoretically deducted in which the variations of modal flexural rigidity and modal neutral axis height are considered. The reference-free damage index is also presented for comparison. Both finite element simulation and experiment investigations were carried out to verify the proposed method. The manufacturing procedure of long-gage fiber Bragg grating (FBG) sensor chosen in the experiment is firstly presented, followed by an experimental study on the essential sensing properties of the long-gage macro-strain sensors and the results verify the excellent sensing properties, in particular the measurement accuracy and dynamic measuring capacity. Modal analysis results of a concrete beam show that the damage appearing in the beam can be well identified by the damage index while the vibration testing results of a RC beam show that the proposed method can not only capture small crack initiation but its propagation. It can be concluded that distributed long-gage dynamic macro-strain sensing technique has great potential for the condition assessment of RC structures subjected to dynamic loading.     

Long distance laser ultrasonic propagation imaging system for damage visualization

Wind turbine blade failure is the most prominent and common type of damage occurring in operating wind turbine systems. Conventional nondestructive testing systems are not available for in situ wind turbine blades. We propose a portable long distance ultrasonic propagation imaging (LUPI) system that uses a laser beam targeting and scanning system to excite, from a long distance, acoustic emission sensors installed in the blade. An examination of the beam collimation effect using geometric parameters of a commercial 2 MW wind turbine provided Lamb wave amplitude increases of 41.5 and 23.1 dB at a distance of 40 m for symmetrical and asymmetrical modes, respectively, in a 2 mm-thick stainless steel plate. With this improvement in signal-to-noise ratio, a feasibility study of damage detection was conducted with a 5 mm-thick composite leading edge specimen. To develop a reliable damage evaluation system, the excitation/sensing technology and the associated damage visualization algorithm are equally important. Hence, our results provide a new platform based on anomalous wave propagation imaging (AWPI) methods with adjacent wave subtraction, reference wave subtraction, reference image subtraction, and the variable time window amplitude mapping method. The advantages and disadvantages of AWPI algorithms are reported in terms of reference data requirements, signal-to-noise ratios, and damage evaluation accuracy. The compactness and portability of the proposed UPI system are also important for in-field applications at wind farms.     

Fast Fourier domain localization algorithm of a single molecule with nanometer precision

We present an algorithm to determine the location of a fluorescent molecule with nanometer-scale accuracy. A Fourier domain localization scheme based on zero-padded fast Fourier transform and phase gradient operators is used to obtain a powerful mathematical model for localizing the molecule without numerical fitting. Compared with conventional algorithms, our position estimator does not require prior background information or initial parameter estimation. Numerical simulations indicate that the proposed method exhibits high localization precision and small bias while executing almost as fast as the fluoroBancroft algorithm.     

基于联合分步APIT定位算法的改进

本文研究了无线传感网络( Wireless Sensor Network,WSNs)的节点定位问题,并针对APIT由于锚节点在低密度环境下的节点误判和节点失效等问题给出了改进,在APICT定位算法的基础提出了联合分步定位算法UNION-APICT(Union Approximate Point-In-Circumcircle Test),该算法是结合连通性的测距技术,RSSI测距技术以及质心定位和APICT等技术,来联合解决对未知节点定位问题。通过仿真实验结果表明,改进后的UNION-APICT在APICT算法的基础之上平均定位误差减少了10%-25%,定位性能有了明显的提升;随着通信半径R和最大探测距离rmax的增加,定位误差也在逐渐减小,该算法较APIT和APICT定位算法在锚节点密度、节点覆盖率和定位精度上都有所提高。     

基于Dini展开的高阶Hankel变换及其在光束传输中的应用

基于Dini级数展开, 导出了p(>0) 阶准离散Hankel变换(the pth-order quasi-discrete Hankel transform based on Dini series expansion, pDQDHT)算法, 并给出了该算法在光束传输中的应用. 通过不同输入函数分别对pDQDHT算法进行测试及光束通过透镜传输的应用实例, 结果表明: pDQDHT算法不仅精度高于现有的Hankel变换算法, 可以进行多次正、逆变换, 能广泛应用于光束分步传输问题, 而且执行速度也与一般的快速Hankel变换算法相当. 关键词： Dini级数展开 高阶Hankel变换 光束传输     

Efficient modal control strategies for active control of vibrations

Some efficient strategies for the active control of vibrations of a beam structure using piezoelectric materials are described. The control algorithms have been implemented for a cantilever beam model developed using finite element formulation. The vibration response of the beam to an impulse excitation has been calculated numerically for the uncontrolled and the controlled cases. The essence of the method proposed is that a feedback force in different modes be applied according to the vibration amplitude in the respective modes i.e., modes having lesser vibration may receive lesser feedback. This weighting may be done on the basis of either displacement or energy present in different modes. This method is compared with existing methods of modal space control, namely the independent modal space control (IMSC), and modified independent modal space control (MIMSC). The method is in fact an extension of the modified independent space control with the addition that it proposes to use the sum of weighted multiple modal forces for control. The proposed method results in a simpler feedback, which is easy to implement on a controller. The procedure is illustrated for vibration control of a cantilever beam. The analytical results show that the maximum feedback control voltage required in the proposed method is further reduced as compared to existing methods of IMSC and MIMSC for similar vibration control. The limitations of the proposed method are discussed.     

差分传声器阵列期望最大化多声源方位估计方法

针对小尺寸传声器阵列多声源方位估计易受混响噪声影响的问题,提出了一种适用于差分传声器阵列的期望最大化多声源方位估计方法。首先,该方法利用期望最大化算法求解出各个时频点瞬时方位估计所应满足的高斯混合模型参数;然后,通过时频点分离技术估计出各声源的方位值。针对现有的硬、软时频点分离技术应用于差分传声器阵列所存在的缺陷,还提出了一种改进的时频点分离方法,该方法融合了软、硬分离方法所具有的优点,有效降低了时频点分离结果对混响噪声的敏感性。仿真和实测实验结果表明:相较于现有的差分传声器阵列多声源估计方法,所提方法在混响噪声环境下具有更高的估计精度和稳健性能。      

A localization approach for multiple sound sources via an expectation maximization algorithm using differential microphone arrays

Conventional sound localization approaches with small-sized microphone arrays are usually sensitive to noise and reverberation. To deal with the problem, an approach based on expectation maximization algorithm with differential microphone arrays(DMAs) is proposed.Firstly, the parameters of Gaussian mixture model for time-frequency instantaneous direction estimation are estimated through the EM algorithm, and then the direction of each sound source is estimated via time-frequency separation. In order to overcome the weakness of existing time-frequency separation techniques, an improved method, which combines the advantages of both the hard and soft separation methods, is also proposed. The improved time-frequency separation method is shown to be less sensitive to noise and reverberation. Simulation and experimental results demonstrate that the proposed localization approach is superior to its existing counterparts in terms of localization accuracy and robustness.