Bone micro-damage assessment using non-linear resonant ultrasound spectroscopy (NRUS) techniques: a feasibility study

Non-linear resonant ultrasound spectroscopy (NRUS) is a technique exploiting the significant non-linear behavior of damaged materials, related to the presence of damage. This study shows for the first time the feasibility of this technique for damage assessment in bone. Two samples of bovine cortical bone were subjected to a progressive damage experiment. Damage accumulation was progressively induced in the samples by mechanical testing. For independent assessment of damage, X-ray CT imaging was performed at each damage step, but only helped in the detection of the prominent cracks. Synchrotron micro-CT imaging and histology using epifluorescence microscopy were performed in one of the two samples at the last damage step and allowed detection of micro-cracks for this step. As the quantity of damage accumulation increased, NRUS revealed a corresponding increase in the non-linear response. The measured change in non-linear response is much more sensitive than the change in elastic modulus. The results suggest that NRUS could be a potential tool for micro-damage assessment in bone. Further work has to be carried out for a better understanding of the physical nature of damaged bone, and for the ultimate goal of in vivo implementation of the technique where bone access will be a challenging problem.     

Equilibrium point damage prognosis models for structural health monitoring

Most structural dynamic systems are of high order; however, they often exhibit phenomena that can be dealt with effectively using low order models. This paper presents a method for describing certain kinds of damage evolution in mechanical systems. The method relies on a simple principle that as damage evolves in a structural dynamic system, the damage indicator (i.e., diagnostic feature) behaves like a stable quasi-stationary equilibrium point in a subsidiary non-linear bifurcating system within the so-called damage center manifold. It is shown that just as linear normal modes govern the behavior of linear structures with idealized damping, so too do non-linear normal forms govern the evolution of damage within structures in many instances. The method is justified with citations from the literature on certain types of mechanical failure and then applied in an experimental case involving reversible damage in a bolted fastener. Off-line experiments on a rotorcraft fuselage show that the evolution of damage is sensitive to both temporal and spatial bifurcation parameters. A diagnostic sensing strategy whereby output-only transmissibility features are used to decrease the order of high order structural dynamic measurements is also described.     

Non-linear realizations of supersymmetry with off-shell central charges

We present a new class of non-linear realizations of the extended supersymmetry algebra with central charges. They were obtained by applying the technique of dimensional reduction by Legendre transformation to a non-linear realization without central charges in one higher dimension. As a result an off-shell central charge is obtained. The non-linear lagrangian is the same as in the case of vanishing central charge. On-shell the central charge vanishes so this non-linear realization differs from that without central charges only off-shell. We work in two dimensions and discuss its extension to higher dimensions.     

Guided waves for autonomous online identification of structural defects under ambient temperature variations

Ultrasonic guided waves that are excited by piezoelectric transducers can be used for the autonomous online identification of structural defects in thin structures. The proposed technique in this paper continuously analyzes a damage metric which is defined as the maximum residual amplitude of the differential signal. A special focus is on the decision making to discriminate the undamaged from the damaged state of the structure where the appropriate detection thresholds are derived statistically from the inverse cumulative distribution function of the damage metric during an initial training phase. An integrated trend analysis by means of the moving average mitigates the impact of statistical outliers and reduces the probability of erroneous identifications.Long-term measurements under ambient temperature variations have been conducted on an aluminum and a composite plate to study the properties of the proposed novelty detection framework. In this process the temperature effect was compensated by the well-known combination of optimal baseline selection (OBS) and baseline signal stretch (BSS). In case of the aluminum structure two artificial cracks with different sizes have been identified reliably. Consistent results were found on the composite specimen where an impact damage was identified for different excitation frequencies.     

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.     

A structural health monitoring strategy using cepstral features

A statistical pattern recognition based damage detection algorithm is proposed. The algorithm is developed according to the training and testing scheme, typical of pattern recognition applications. The original contribution of the work is given by the use of an adaptation of Mel-Frequency Cepstral Coefficients as damage sensitive features, as their compactness and de-correlation characteristics make them particularly suited for statistical pattern recognition applications. At the same time, the ease of extraction, which requires minimal user expertise, represents an important advantage over other more popular features, and makes the cepstral features particularly convenient for implementation into automatic structural health monitoring routines. The damage detection algorithm employs the squared Mahalanobis distance to solve the Structural Health Monitoring assignment. The method is validated by using both simulated and experimental data, and the performance of said features is compared to that of Auto-Regressive (AR) coefficients, which have been largely used to solve the task of structural damage detection. The experimental data were measured on a steel frame, which behave nonlinearly in its damaged configuration, at the Los Alamos National Laboratory. Results demonstrate that the proposed approach may be conveniently used in real-life applications, since cepstral features outperform AR coefficients when dealing with experimental data modeled to mimic the operational and environmental variability.     

Hysteresis in structural dynamics

In this paper the Preisach hysteresis model is applied to determine the dynamic behavior of a steel column with mass on the top and loaded by an impulse force. The column is considered as a rigid element, while the fixed end of the column is modeled with a rotational spring of hysterestic characteristic. In the solution of the non-linear dynamical equation of motion the fix-point technique is inserted to the time marching iteration. In the investigation the non-linearity of the rotation spring is modeled with the Preisach hysteresis model. The variation of amplitude and the action time interval of force are changing. The results are plotted in figures.     

FRF-based structural damage detection of controlled buildings with podium structures: Experimental investigation

How to use control devices to enhance system identification and damage detection in relation to a structure that requires both vibration control and structural health monitoring is an interesting yet practical topic. In this study, the possibility of using the added stiffness provided by control devices and frequency response functions (FRFs) to detect damage in a building complex was explored experimentally. Scale models of a 12-storey main building and a 3-storey podium structure were built to represent a building complex. Given that the connection between the main building and the podium structure is most susceptible to damage, damage to the building complex was experimentally simulated by changing the connection stiffness. To simulate the added stiffness provided by a semi-active friction damper, a steel circular ring was designed and used to add the related stiffness to the building complex. By varying the connection stiffness using an eccentric wheel excitation system and by adding or not adding the circular ring, eight cases were investigated and eight sets of FRFs were measured. The experimental results were used to detect damage (changes in connection stiffness) using a recently proposed FRF-based damage detection method. The experimental results showed that the FRF-based damage detection method could satisfactorily locate and quantify damage.     

Sensitivity enhancement in structural measurements by solid state NMR through pulsed spin locking

Free induction decay (FID) signals in solid state NMR measurements performed with magic angle spinning can often be extended in time by factors on the order of 10 by a simple pulsed spin locking technique. The sensitivity of a structural measurement in which the structural information is contained in the dependence of the integrated FID amplitude on a preceding evolution period can therefore be enhanced substantially by pulsed spin locking in the signal detection period. We demonstrate sensitivity enhancements in a variety of solid state NMR techniques that are applicable to selectively isotopically labeled samples, including 13C-15N rotational echo double resonance (REDOR), 13C-13C dipolar recoupling measurements using the constant-time finite-pulse radio-frequency-driven recoupling (fpRFDR-CT) and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) techniques, and torsion angle measurements using the double quantum chemical shift anisotropy (DQCSA) technique. Further, we demonstrate that the structural information in the solid state NMR data is not distorted by pulsed spin locking in the detection period.     

Sequential structural damage diagnosis algorithm using a change point detection method

This paper introduces a damage diagnosis algorithm for civil structures that uses a sequential change point detection method. The general change point detection method uses the known pre- and post-damage feature distributions to perform a sequential hypothesis test. In practice, however, the post-damage distribution is unlikely to be known a priori, unless we are looking for a known specific type of damage. Therefore, we introduce an additional algorithm that estimates and updates this distribution as data are collected using the maximum likelihood and the Bayesian methods. We also applied an approximate method to reduce the computation load and memory requirement associated with the estimation. The algorithm is validated using a set of experimental data collected from a four-story steel special moment-resisting frame and multiple sets of simulated data. Various features of different dimensions have been explored, and the algorithm was able to identify damage, particularly when it uses multidimensional damage sensitive features and lower false alarm rates, with a known post-damage feature distribution. For unknown feature distribution cases, the post-damage distribution was consistently estimated and the detection delays were only a few time steps longer than the delays from the general method that assumes we know the post-damage feature distribution. We confirmed that the Bayesian method is particularly efficient in declaring damage with minimal memory requirement, but the maximum likelihood method provides an insightful heuristic approach.     

Saturated patterned excitation microscopy with two-dimensional excitation patterns

The techniques of patterned excitation microscopy (PEM, also referred to in the literature as structured illumination, harmonic excitation light microscopy, or laterally modulated excitation microscopy), has recently been extended to the non-linear regime, permitting a further increase in resolution breaking the Abbe diffraction limit (saturated PEM, saturated patterned excitation microscopy (SPEM)). Fluorescence saturation was suggested as the non-linear effect employed to achieve this aim. Here a two-dimensional extension of the linear and the non-linear patterned excitation technique is introduced and simulations of the expected resolution improvement are presented. The simulations account for photon statistics, a sub-optimal degree of modulation and a high amount of background fluorescence in the sample. The resulting point-spread-functions achieve a full width at half maximum of 215 nm (widefield), 118 nm (linear PEM), and 57 nm (saturated PEM, 9x9 orders). For higher resolution, an increased number of detected photons and of raw data images are required. A potential method for substantially decreasing the required number of raw images in PEM and SPEM is discussed.     

Using the Complex Jacobi Method to Simulate Kerr Non-linear Photonic Components

The iterative complex Jacobi technique has been extended to simulate the third order Kerr effect in wavelength scale dielectric structures. This method solves the Helmholtz equation in a discrete finite simulation space by an iterative process. An update equation refines the field values at each iteration step, until a desired accuracy is achieved. We have extended the iterative process with an extra calculation step which allows simulating materials with the non-linear third order Kerr effect. Our adjustment of the discrete field operators in the update equation also introduces PMLs as absorbing boundaries and the total field/scattered field formalism as field source for this method.     

Damage localisation in plate like-structures using the two-dimensional polynomial annihilation edge detection method

The topic of non-destructively detecting localised damage in plates is addressed in this article. Since the presence of a crack or a delamination causes a discontinuity in the mode shape first derivatives, a numerical method for detecting discontinuities in smooth piecewise functions and their derivatives, based on a polynomial-annihilation technique is presented. The method, already proposed for beam-type structures, has been extended to enable the detection and localisation of damage in plate-like structures for which only post-damage mode shapes are available. Applying finite element analysis, the mode shapes of an isotropic plate with a saw-cut and a multi-layered composite plate with a delamination have been calculated and the performance of the approach evaluated for increasing amounts of noise. Encouraging results indicate that further development of the technique for non-destructive testing of plate-like structures would be highly worthwhile.     

Fan broadband noise shielding for over-wing engines

Increasingly demanding community noise targets are promoting noise performance ever higher on the list of airliner design drivers. In response, significant noise reductions are being made, though at a declining rate—it appears that a whole airframe approach is now needed to achieve significant further gains. As a possible step in this direction, over-wing engine installations are considered here, which use the airframe itself as a noise shield. The paper is the account of an experimental investigation of the comparative shielding performances of a range of relative engine positions on such a layout. Using the statistical modelling technique Kriging, we build an approximation of the noise shielding metric as a function of the position of the engines above the wing—this can serve as the input to multi-disciplinary design trade-off studies. We then compare the results found with the results of applying simple half-barrier diffraction theory to the same problem. We conclude that the latter could be considered as a first order, conceptual design tool, though it misses certain features of the design merit landscape identified by the experiment presented here.     

Sensitivity analysis of an auto-correlation-function-based damage index and its application in structural damage detection

Structural damage detection using time domain vibration responses has advantages such as simplicity in calculation and no requirement of a finite element model, which attracts more and more researchers in recent years. In present paper, a new approach to detect the damage based on the auto correlation function is proposed. The maximum values of the auto correlation function of the vibration response signals from different measurement points are formulated as a vector called Auto Correlation Function at Maximum Point Value Vector, AMV for short. The relative change of the normalized AMV before and after damage is used as the damage index to locate the damage. Sensitivity analysis of the normalized AMV with respect to the local stiffness shows that the normalized AMV has a sharp change around the local stiffness change location, which means the normalized AMV is a good indicator to detect the damage even when the damage is very small. Stiffness reduction detection of a 12-story frame structure is provided to illustrate the validity, effectiveness and the anti-noise ability of the proposed method. Comparison of the normalized AMV and the other correlation-function-based damage detection method shows the normalized AMV has a better detectability.     

Limit cycle oscillation of missile control fin with structural non-linearity

Non-linear aeroelastic characteristics of a deployable missile control fin with structural non-linearity are investigated. A deployable missile control fin is modelled as a two-dimensional typical section model. Doublet-point method is used for the calculation of supersonic unsteady aerodynamic forces, and aerodynamic forces are approximated by using the minimum-state approximation. For non-linear flutter analysis structural non-linearity is represented by an asymmetric bilinear spring and is linearized by using the describing function method. The linear and non-linear flutter analyses indicate that the flutter characteristics are significantly dependent on the frequency ratio. From the non-linear flutter analysis, various types of limit cycle oscillations are observed in a wide range of air speeds below or above the linear divergent flutter boundary. The non-linear flutter characteristics and the non-linear aeroelastic responses are investigated.     

Use of optimization in helicopter vibration control by structural modification

The application of a mathematical optimization process to helicopter vibration control by structural modification is described. Attention is focused on the reduction of vibration in the crew area. With stiffness parameters as design variables, use is made of forced vibration response circles to identify the parameters most effective in controlling the response in the crew area, thereby reducing the number of available design variables to a tractable size. The problem of reducing vibration is then cast as a non-linear programming problem and a sequential unconstrained minimization technique incorporating an algorithm based on the methods of Davidon, Fletcher and Powell is used to determine the precise values of the parameters. The method is applied to a simple two-dimensional beam-element helicopter fuselage model and the results discussed. Although the model is too simple for useful deductions of practical significance to be made in the strictly engineering sense, the exercise does demonstrate what can and cannot be done in controlling vibration by using an optimization routine.     

兰姆波结构健康监测中的概率损伤成像

应用概率成像方法对兰姆波结构健康监测中板的损伤进行识别。根据兰姆波损伤散射信号的传播时间以及传感器网络中一对发射-接收传感器的空间位置来确定一个椭圆轨迹,该轨迹显示了损伤可能出现的位置。将监测区域均匀网格化,计算各网格节点到椭圆轨迹的最短距离,将此距离映射为损伤出现的概率。采用灰度等级对所有网格节点处的概率值进行量化,则由每一个发射接收传感器对就确定了一个灰度图像。为了突出损伤,应用图像融合技术对传感器网络中所有发射接收传感器对所构成的灰度图像进行融合。对铝板中横穿孔损伤的实验结果显示了该方法能够有效地确定损伤的位置和范围,有助于推动兰姆波结构健康监测的实用化。