A reconstruction method using geometric subdivision and NURBS interpolation

Subdivision surfaces (SubD, NURSS) construction is a popular method to present and animate sculpture shapes for entertainment, and this is preferred due to advantage of polygon mesh. But subdivision surfaces have limited familiarity and portability in modern CAD, unlike NURBS-based entities. NURBS-based sculpting using dense point cloud data obtained through geometric subdivision has been so far a less discussed topic. The current work discusses the new methodology of using geometric subdivision and NURBS interpolation with an aim to add a new dimension to reverse engineering. This has distinct advantages like accurate shape building using scanned data, manufacturing ability of complex shapes, faster and accurate shape representation with high quality surfaces, model portability, and a better control on object shape and better patch-planning. Major milestones of the work are bridging the geometric subdivision and NURBS reconstruction on subdivided data, NURBS patch and topology planning (straight and PDPA scan), construction of trimmed NURBS surfaces and, finally, writing IGES of resultant patches. The work is a high-level automation solution for complex constructions. It is applied on human head-scan data and results are displayed.     

应变模态振型获取的一种简便方法

根据应变模态分析原理,定义了一个新的应变模态振型系数,提出了基于应变响应获取结构应变模态振型的一种简便方法,并通过简支梁实验进行了验证。研究结果表明,采用该方法无需测量位移模态,仅需采用单点激励,用电阻应变计测量结构上各测点的应变响应信息,即可获得被测结构应变模态振型,大大简化了应变模态在工程结构损伤识别中的实验检测分析过程。     

Improvement of damage detection methods based on experimental modal parameters

The objective of this paper is to introduce a new method for structural damage detection based on experimentally obtained modal parameters. The new method is suitable for detection of fatigue damage occurring in an aluminium cantilever beam. The damage has been practically realised as saw cuts of different sizes and at different locations. The first step of analysis included an attempt of damage identification with the most often used damage indicators based on measured modal parameters. For that purpose special signal processing technique has been proposed improving the effectiveness of indicators tested. However the results obtained have not been satisfactory. That was the motivation for defining new damage indicators (frequency change based damage indicator, Hybrid Damage Detection method), utilising the change of natural frequencies and any mode shape (measured or modelled) as the measurement of frequencies is much less time consuming in comparison to total mode shape measurement. It has been shown that the proposed technique is suitable for damage localisation in beam-like structures.     

Model updating of damped structures using FRF data

Due to the important contribution of damping on structural vibration, model updating of damped structures becomes significant and remains an issue in most model updating methods developed to date. In this paper, the frequency response function(FRF) method, which is one of the most frequently referenced model updating methods, has been further developed to identify damping matrices of structural systems, as well as mass and stiffness matrices. In order to overcome the problem of complexity of measured FRF and modal data, complex updating formulations using FRF data to identify damping coefficients have been established for the cases of proportional damping and general non-proportional damping. To demonstrate the effectiveness of the proposed complex FRF updating method, numerical simulations based on the GARTEUR structure with structural damping have been presented. The updated results have shown that the complex FRF updating method can be used to derive accurate updated mass and stiffness modelling errors and system damping matrices.     

On-line fan blade damage detection using neural networks

This paper presents a methodology for monitoring the on-line condition of axial-flow fan blades with the use of neural networks. In developing this methodology, the first stage was to utilise neural networks trained on features extracted from on-line blade vibration signals measured on an experimental test structure. Results from a stationary experimental modal analysis of the structure were used for identifying global blade mode shapes and their corresponding frequencies. These in turn were used to assist in identifying vibration-related features suitable for neural network training. The features were extracted from on-line blade vibration and strain signals which were measured using a number of sensors.The second stage in the development of the methodology entails utilising neural networks trained on numerical Frequency Response Function (FRF) features obtained from a Finite Element Model (FEM) of the test structure. Frequency domain features obtained from on-line experimental measurements were used to normalise the numerical FRF features prior to neural network training. Following training, the networks were tested using experimental frequency domain features. This approach makes it unnecessary to damage the structure in order to train the neural networks.The paper shows that it is possible to classify damage for several fan blades by using neural networks with on-line vibration measurements from sensors not necessarily installed on the damaged blades themselves. The significance of this is that it proves the possibility to perform on-line fan blade damage classification using less than one sensor per blade. Even more significant is the demonstration that an on-line damage detection system for a fan can be developed without having to damage the actual structure.     

A frequency response based structural damage localization method using independent component analysis

Vibration-based structural damage detection has been the focus of attention by many researchers over the last few decades. However, most methods proposed for this purpose utilize extracted modal parameters or some indices constructed on the basis these parameters. Our literature review revealed that few papers have employed frequency response functions (FRFs) for detecting structural damage. In this paper, a technique is presented for damage detection which is based on measured FRFs. Independent component analysis (ICA) has been implemented on the spatiotemporal responses in each frequency in order to reduce the dimension of the data. This is based on the concept that the forced harmonic response of a linear vibrating system can be fully captured utilizing a single ICA mode. A different approach is also presented in which ICA is applied to the frequency domain data. Operational deflection shapes (ODSs) have been decomposed using ICA to localize the damage. The efficiency of both methods is demonstrated through some numerical and experimental case studies.     

Analysis of swept-sine runs during modal identification

Experimental modal analysis of large aerospace structures in Europe combine nowadays the benefits of the very reliable but time-consuming phase resonance method and the application of phase separation techniques evaluating frequency response functions (FRF). FRFs of a test structure can be determined by a variety of means. Applied excitation signal waveforms include harmonic signals like stepped-sine excitation, periodic signals like multi-sine excitation, transient signals like impulse and swept-sine excitation, and stochastic signals like random. The current article focuses on slow swept-sine excitation which is a good trade-off between magnitude of excitation level needed for large aircraft and testing time. However, recent ground vibration tests (GVTs) brought up that reliable modal data from swept-sine test runs depend on a proper data processing. The article elucidates the strategy of modal analysis based on swept-sine excitation. The standards for the application of slowly swept sinusoids defined by the international organisation for standardisation in ISO 7626 part 2 are critically reviewed. The theoretical background of swept-sine testing is expounded with particular emphasis to the transition through structural resonances. The effect of different standard procedures of data processing like tracking filter, fast Fourier transform (FFT), and data reduction via averaging are investigated with respect to their influence on the FRFs and modal parameters. Particular emphasis is given to FRF distortions evoked by unsuitable data processing. All data processing methods are investigated on a numerical example. Their practical usefulness is demonstrated on test data taken from a recent GVT on a large aircraft. The revision of ISO 7626 part 2 is suggested regarding the application of slow swept-sine excitation. Recommendations about the proper FRF estimation from slow swept-sine excitation are given in order to enable the optimisation on these applications for future modal survey tests of large aerospace structures.     

Structural Damage Detection Method Based on Decomposition of the Operating Deflection Shapes

Full-field measurement techniques such as the scanning laser Doppler vibrometer (LDV) and the electronic speckle pattern interferometry systems can provide a dense and accurate vibration measurement on structural operating deflection shape (ODS) on a relatively short period of time.The possibility of structural damage detection and localization using the ODS looks likely more attractive than when using traditional measurement techniques which address only a small number of discrete points.This paper discusses the decomposition method of the structural ODSs in the time history using principal component analysis to provide a novel approach to the structural health monitoring and damage detection.The damage indicator is proposed through comparison of structural singular vectors of the ODS variation matrixes between the healthy and damaged stages.A plate piece with a fix-free configuration is used as an example to demonstrate the effectiveness of the damage detection and localization using the proposed method.The simulation results show that:(1) the dominated principal components and the corresponding singular vectors obtained from the decomposition of the structural ODSs maintain most of all vibration information of the plate,especially in the case of harmonic force excitations that the 1st principal component and its vectors mostly dominated in the system;(2) the damage indicator can apparently flag out the damage localization in the case of the different sinusoidal excitation frequencies that may not be close to any of structural natural frequencies.The successful simulation indicates that the proposed method for structural damage detection is novel and robust.It also indicates the potentially practical applications in industries.     

频响函数在结构损伤检测中应用的试验研究

结构动力测试中,频响函数可直接测得,不仅避免了在模态提取时的误差,而且在相同频段上可提供更多结构损伤信息,因此可方便地应用于结构损伤的检测中。对于结构基础的随机激励,试验结果表明频响函数法可有效地检测结构的损伤。同时说明传感器布置在结构的不同位置都可检测结构的损伤。并且随机振动的大小不影响结构损伤检测的效果。为频响函数法在现场实测结构的损伤提供了依据。     

Novel Laplacian scheme and multiresolution modal curvatures for structural damage identification

Modal curvature is more sensitive to structural damage than directly measured mode shape, and the standard Laplace operator is commonly used to acquire the modal curvatures from the mode shapes. However, the standard Laplace operator is very prone to noise, which often leads to the degraded modal curvatures incapable of identifying damage. To overcome this problem, a novel Laplacian scheme is proposed, from which an improved damage identification algorithm is developed. The proposed step-by-step procedures in the algorithm include: (1) By progressively upsampling the standard Laplace operator, a new Laplace operator is constructed, from which a Laplace operator array is formed; (2) by applying the Laplace operator array to the retrieved mode shape of a damaged structure, the multiresolution curvature mode shapes are produced, on which the damage trait, previously shadowed under the standard Laplace operator, can be revealed by a ridge of multiresolution modal curvatures; (3) a Gaussian filter is then incorporated into the new Laplace operator to produce a more versatile Laplace operator with properties of both the smoothness and differential capabilities, in which the damage feature is effectively strengthened; and (4) a smoothened nonlinear energy operator is introduced to further enhance the damage feature by eliminating the trend interference of the multiresolution modal curvatures, and it results in a significantly improved damage trait. The proposed algorithm is tested using the data generated by an analytical crack beam model, and its applicability is validated with an experimental program of a delaminated composite beam using scanning laser vibrometer (SLV) to acquire mode shapes. The results are compared in each step, showing increasing degree of improvement for damage effect. Numerical and experimental results demonstrate that the proposed novel Laplacian scheme provides a promising damage identification algorithm, which exhibits apparent advantages (e.g., high-noise insusceptibility, insightful in damage revealment, and visualized damage presentation) over the standard Laplace operator.     

Development of scanning damage index for the damage detection of plate structures using modal strain energy method

This work presents a novel approach of nondestructive detection of damage in plate structures by using experimental modal analysis (EMA) and modal strain energy method (MSEM). An aluminum alloy 6061 thin plate with a surface crack is investigated in this study. EMA is conducted on the plate to obtain the mode shapes before and after damage. The modal displacements of each mode shape are then used to compute the modal strain energy. For all measured mode shapes, a damage index is defined by using the ratio of modal strain energies of the plate before and after damage. In fact, small damage causes very little change in system response, but it is an essential early warning of structure damage. As the second-order derivatives, modal strain energy is much more sensitive to the small change of structural response than frequencies and mode shapes. It is therefore feasible to approach the small damage by using a damage index defined by fractional MSE of the structure before and after damage. In this study, a scanning damage index (SDI) is developed by moving damage indices obtained from the local area throughout the structure as if a scanning sensor is used to inspect the structure. The damage indices in overlap areas are added up and the summation may intensify the signals of damage in the plate. Limited by the numbers of measured point, a differential quadrature method is employed to calculate the partial differential terms in strain energy formula. Experimental results show that SDI well identifies a surface crack location by using only few measured mode shapes of the aluminum plate. This novel approach provides a flexible, cost-effective, and nondestructive damage evaluation in either local or global structure. Its applicability to different types of structures and different sizes of damage is to be experimentally validated in the future work.     

改进的特征值灵敏度在结构损伤识别中的应用

传统的特征值灵敏度分析中忽略了振型变化的影响,导致特征值灵敏度难以准确地识别出结构损伤。为提高特征值灵敏度的准确性,利用未损伤结构的振型线性表示损伤情况下结构振型的变化,进而改进了特征值灵敏度的理论分析方法。在不同的损伤工况下,计算数值模型改进前后的特征值灵敏度,验证表明改进后的特征值灵敏度具有更高的精度。以孔洞直径和位置均未知的实际结构为研究对象,利用改进后灵敏度方法准确识别了结构损伤的位置和程度,与结构的孔洞直径和位置实测值相吻合,表明了改进后灵敏度方法具有准确实用性,从而弥补了传统特征值灵敏度法在结构损伤识别中的缺陷。     

Time-domain analysis of piezoelectric impedance-based structural health monitoring using multilevel wavelet decomposition

A new approach to analyze the response from a piezoelectric wafer in an impedance-based structural health monitoring (SHM) method is proposed. It is shown that the time-domain response of a piezoceramic wafer provides information on the electromechanical impedance (EMI) variation when a monitored structure is damaged. Practical analysis was carried out using wavelet transform in two different levels. This approach simplifies EMI based SHM and the results show that it is more sensitive to damage than methods based on impedance measurements in the frequency domain. The efficiency of this new approach is demonstrated through experiments using an aluminum plate. The piezoelectric wafer was excited using a chirp signal and its response was analyzed using both frequency response functions (FRF) and the proposed method. The results confirm that this new approach is more sensitive to detect damage than FRF based methods.     

Cyclostationarity and the cepstrum for operational modal analysis of MIMO systems—Part II: Obtaining scaled mode shapes through finite element model updating

This paper presents a new technique for scaling mode shapes, obtained from cepstrum-based operational modal analysis (OMA) techniques, such as that described in the companion paper, using finite element model updating. This OMA technique estimated frequency response functions (FRFs) between a cyclostationary input and response measurements. If the input is frequentially white, the resulting FRFs can be obtained up to an overall scaling constant using the in-band poles and zeros identified in the OMA process and employing the response autospectrum as a reference to correct for the effect of out of band modes. In this way, the mode shapes would be scaled correctly relative to each other but would still have arbitrary overall magnitude. If the input is not white, then no reference is available to correct FRF regenerated from in-band poles and zeros, and so these FRFs will exhibit both an overall slope resulting from the effect of out-of-band poles and zeros, and an arbitrary magnitude. This overall slope will differ between measurement locations so even the relative scaling between the mode shapes will be lost. This paper describes a simple technique for recovering both the relative and overall scaling of the FRFs, and hence the mode shapes, based on finite element model updating.     

An experimental study on damage detection of structures using a timber beam

Using vibration methods for the damage detection and structural health monitoring in bridge structures is rapidly developing. However, very little work has so far been reported on timber bridges. This paper intends to address such shortcomings by experimental investigation on a timber beam using a vibration based method to detect damage. A promising damage detection algorithm based on modal strain energy was adopted and modified to locate/evaluate damage. A laboratory investigation was conducted on a timber beam inflicted with various damage scenarios using modal tests. The modal parameters obtained from the undamaged and damaged state of the test beam were used in the computation of damage index, were then applied using a damage detection algorithm utilising modal strain energy and a statistical approach to detect location of damage. A mode shape reconstruction technique was used to enhance the capability of the damage detection algorithm with limited number of sensors. The test results and analysis show that location of damage can be accurately identified with limited sensors. The modified method is less dependent on the number of modes selected and can detect damage with a higher degree of confidence.     

Damage identification by response surface based model updating using D-optimal design

Statistical tools, as well as mathematical ones, have been widely adopted and their performance has been shown in different engineering problems where randomicity usually exists. In the realm of engineering, merging statistical analysis into structural evaluation and assessment will be a tendency in the future. As a combination of mathematical and statistical techniques, response surface methodology has been successfully applied to design optimization, response prediction and model validation. This methodology provides explicit functions to represent the relationships between the inputs and outputs of a physical system, which is also a desirable advantage in damage identification. However, so far little research has been carried out in applying the response surface methodology to structural damage identification. This paper presents a damage identification method achieved by response surface based model updating using D-optimal designs. Compared with some common designs constructing response surfaces, D-optimal designs generally require a minimum number of numerical samples and this merit is quite desirable when analysts cannot obtain enough samples. In this study, firstly D-optimal designs are used to establish response surface models for screening out non-significant updating parameters and then first-order response surface models are constructed to substitute for finite element models in predicting the dynamic responses of an intact or damaged physical system. Three case studies of a numerical beam, a tested reinforced concrete frame and a tested full-scale bridge have been used to verify the proposed method. Physical properties such as Young’s modulus and section inertias were chosen as the input features and modal frequency was the only response feature. It has been observed that the proposed method gives enough accuracy in damage prediction of not only the numerical but also the real-world structures with single and multiple damage scenarios, and the first-order response surface models based on the D-optimal criterion are adequate for such damage identification purposes.     

Vibration based damage detection using large array sensors and spatial filters

In this paper, a novel approach for vibration based damage detection is proposed. The approach relies on the use of a large network of sensors (possibly hundreds of them) to which a programmable linear combiner is attached. The linear combiner is programmed to work as a modal filter. The frequency content of the output of the modal filter is proposed as feature for damage detection. It is shown that if a local damage is present, spurious peaks appear in the FRF of the modal filter whereas if temperature changes are considered, the FRF of the modal filter is shifted but its shape remains unchanged. The approach is interesting because of the ability to differentiate between local damage and global environmental changes to a structure. Issues about the practical implementation of the method are discussed.     

Damage identification by multi-model updating in the modal and in the time domain

Computational model updating techniques are used to adjust selected parameters of finite element models in order to make the models compatible with experimental data. This is done by minimizing the differences (residuals) of analytical and experimental data, for example, natural frequencies and mode shapes by numerical optimization procedures. For a long-time updating techniques have also been investigated with regard to their ability to localize and quantify structural damage. The success of such an approach is mainly governed by the quality of the damage model and its ability to describe the structural property changes due to damage in a physical meaningful way. Our experience has shown that due to unavoidable modelling simplifications and measurement errors the changes of the corresponding damage parameters do not always indicate structural modifications introduced by damage alone but indicate also the existence of other modelling uncertainties which may be distributed all over the structure. This means that there are two types of parameters which have to be distinguished: the damage parameters and the other parameters accounting for general modelling and test data uncertainties. Although these general parameters may be physically meaningless they are necessary to achieve a good fit of the test data and it might happen that they cannot be distinguished from the damage parameters. For complex industrial structures it is seldom possible to generate unique structural models covering all possible damage scenarios so that one has to expect, that the parameters introduced for describing the damage will not be fully consistent with the physical reality. Even then the change of such parameters identified from test data taken continuously or temporarily over the time may serve as a feature for structural health monitoring. It is well known that low-frequency modal test data or static response data are not very well suited for detecting and quantifying localized small size damage. Time domain response data from impact tests carry high-frequency information which usually is lost when experimental modal data are utilized for damage identification. Even so only little literature was found addressing the utilization of experimental time histories for model updating in conjunction with damage identification.In the present paper we summarize the methodology of computational model updating and report about our experience with damage identification using two different model updating techniques. The first is based on classical modal residuals (natural frequencies and mode shapes) which is extended to allow for simultaneous updating of two models, one for the initial undamaged structure and the second for the damaged structure using the test data of both states (multi-model updating). The second technique uses residuals composed of measured and analytical time histories. Time histories have the advantage of carrying high-frequency information which is beneficial for the detection of local damage and which usually is lost when modal residuals are used. Both techniques have been applied to the same beam structure consisting of two thin face sheets which were bonded together by an adhesive layer. It was the aim of this application to study the performance of the two techniques to localize and quantify the damage which was introduced locally in the adhesive layer.     

Rapid localization of damage using a circular sensor array and Lamb wave based triangulation

A damage detection and imaging methodology based on symmetry of neighborhood sensor path and similarity of signal patterns with respect to radial paths in a circular array of sensors has been developed. It uses information regarding Lamb wave propagation along with a triangulation scheme to rapidly locate and quantify the severity of damage without using all of the sensor data. In a plate like structure, such a scheme can be effectively employed besides full field imaging of wave scattering pattern from the damage, if present in the plate. This new scheme is validated experimentally. Hole and corrosion type damages have been detected and quantified using the proposed scheme successfully. A wavelet based cumulative damage index has been studied which shows monotonic sensitivity against the severity of the damage, which is most desired in a Structural Health Monitoring system.     

一种新的频响函数无偏估计方法

在对几种典型的频响函数估计进行分析的基础上，利用不相关信号的互功率谱多次平均趋于零的性质，提出了一种新的频响函数无偏估计方法。该估计方法不需要测试第3个信号即可达到无偏估计的目的，避免了测试系统过于复杂，减小了测试工作量和因过多环节的引入而降低估计精度的可能性。测试n组数据，可以进行n(n—1)／2次平均，平均次数是其他方法的(n—1)／2倍，提高了频响函数估计的精度。