Wieslaw Ostachowicz

Fractal dimension analysis of higher-order mode shapes for damage identification of beam structures

Fractal dimension analysis is an emerging method for vibration-based structural damage identification. An unresolved problem in this method is its incapability of identifying damage by higher-order mode shapes. The natural inflexions of higher-order mode shapes may cause false peaks of high-magnitude estimates of fractal dimension, largely masking any signature of damage. In the situation of a scanning laser vibrometer (SLV) providing a chance to reliably acquire higher-order (around tenth-order) mode shapes, an improved fractal dimension method that is capable of treating higher-order mode shapes for damage detection is of important significance. This study proposes a sophisticated fractal dimension method with the aid of a specially designed affine transformation that is able to obviate natural inflexions of a higher-order mode shape while preserving its substantial damage information. The affine transformed mode shape facilitates the fractal dimension analysis to yield an effective damage feature: fractal dimension trajectory, in which an abruptly risking peak clearly characterizes the location and severity of the damage. This new fractal dimension method is demonstrated on multiple cracks identification in numerically simulated damage scenarios. The effectiveness of the method is experimentally validated by using a SLV to acquire higher-order mode shapes of a cracked cantilever beam.

Damage detection in plates using two-dimensional directional Gaussian wavelets and laser scanned operating deflection shapes

Mode shape analysis by wavelet transform has been used effectively for vibration-based damage detection in plates. As an extension of previous studies, this study focuses on an improved method for damage detection in plates: scrutiny of operating deflection shapes by two-dimensional directional Gaussian wavelet transforms. With this method, the proposed two-dimensional directional Gaussian wavelet can characterize directional information about damage; moreover, the operating deflection shapes can be used to address the real-time dynamic characteristics of a plate. To identify damage, the local surface of the plate is scanned using a scanning laser vibrometer to generate the local operating deflection shape, which is interrogated by two-dimensional directional Gaussian wavelets for damage. The feasibility of the method is numerically demonstrated using a low-magnitude operating deflection shape of a two-sided clamped plate, incorporating white noise with signal-to-noise ratio of 40 dB. The applicability of the method is then experimentally validated by detecting a cross-like notch in a suspended aluminum plate with the operating deflection shapes measured by a scanning laser vibrometer. Numerical and experimental results show that the method is capable of revealing directional features of small damage with high precision and strong robustness against noise. It appears that this damage detection method is related only to the spatially distributed measurement of vibrational responses in local critical regions of the plate. With this local property, the method requires no numerical or physical benchmark models for the entire structure in question nor any prior knowledge of either the material properties or the boundary conditions of the structure. (The Matlab code performing directional Gaussian wavelet transform can be provided by the corresponding author as per request.)

The use of electromechanical impedance conductance signatures for detection of weak adhesive bonds of carbon fibre–reinforced polymer

The joints between structural elements should ensure safe usage of the structure. One of the joining method is based on adhesive bonding. However, adhesive bonding has not replaced riveting yet. Rivets are still present even in newest composite aircraft AIRBUS 350. The reliability of the adhesive bonding limits the use of adhesive bonding for primary aircraft structures and there is a search for new non-destructive testing tools allowing to (1) assessment of the surfaces before bonding and (2) assessment of the adhesive bond. The performance of adhesive bonds depends on the physico-chemical properties of the bonded surfaces. The contamination leading to weak bonds may have various origin and be caused by contamination (moisture, release agent, hydraulic fluid and fuel) or poor curing of adhesive. In this work, the research is focused on the development of the method for assessment of the adhesive bonds. Bonded carbon fibre–reinforced polymer samples were considered. Electromechanical impedance technique was proposed. The technique is based on electrical impedance measurements of a piezoelectric transducer attached to the investigated structure. The piezoelectric effect causes the electrical response of a piezoelectric transducer to be related to mechanical response of the structure. The indexes for comparison of the conductance spectra were proposed. Three different cases of possible weak bonds were selected for the investigation. The same cases were investigated by destructive methods by other authors. Such approach allows for direct comparison of the obtained results. It was shown that the proposed method allows for clear separation of weak bond cases from the cases for other samples and free sensors. In terms of weak bond assessment, the frequency change with weak bond level (contamination and level of poor curing) was observed. The obtained results are promising and encourage to future research.

An adaptive wing for a small-aircraft application with a configuration of fibre Bragg grating sensors

In this paper a concept of an adaptive wing for small-aircraft applications with an array of fibre Bragg grating (FBG) sensors has been presented and discussed. In this concept the shape of the wing can be controlled and altered thanks to the wing design and the use of integrated shape memory alloy actuators. The concept has been tested numerically by the use of the finite element method. For numerical calculations the commercial finite element package ABAQUS® has been employed. A finite element model of the wing has been prepared in order to estimate the values of the wing twisting angles and distributions of the twist for various activation scenarios. Based on the results of numerical analysis the locations and numbers of the FBG sensors have also been determined. The results of numerical calculations obtained by the authors confirmed the usefulness of the assumed wing control strategy. Based on them and the concept developed of the adaptive wing, a wing demonstration stand has been designed and built. The stand has been used to verify experimentally the performance of the adaptive wing and the usefulness of the FBG sensors for evaluation of the wing condition.

Crack detection in beams in noisy conditions using scale fractal dimension analysis of mode shapes

Fractal dimension analysis of mode shapes has been actively studied in the area of structural damage detection. The most prominent features of fractal dimension analysis are high sensitivity to damage and instant determination of damage location. However, an intrinsic deficiency is its susceptibility to measurement noise, likely obscuring the features of damage. To address this deficiency, this study develops a novel damage detection method, scale fractal dimension (SFD) analysis of mode shapes, based on combining the complementary merits of a stationary wavelet transform (SWT) and Katz’s fractal dimension in damage characterization. With this method, the SWT is used to decompose a mode shape into a set of scale mode shapes at scale levels, with damage information and noise separated into distinct scale mode shapes because of their dissimilar scale characteristics; the Katz’s fractal dimension individually runs on every scale mode shape in the noise-adaptive condition provided by the SWT to canvass damage. Proof of concept for the SFD analysis is performed on cracked beams simulated by the spectral finite element method; the reliability of the method is assessed using Monte Carlo simulation to mimic the operational variability in realistic damage diagnosis. The proposed method is further experimentally validated on a cracked aluminum beam with mode shapes acquired by a scanning laser vibrometer. The results show that the SFD analysis of mode shapes provides a new strategy for damage identification in noisy conditions.

Delamination localization in wind turbine blades based on adaptive time-of-flight analysis of noncontact laser ultrasonic signals

Abstract In this study, a two-level scanning strategy for a noncontact laser ultrasonic measurement system is proposed to expedite the inspection of a wind turbine blade. First, coarse scanning of the entire blade is performed with a low spatial resolution for initial delamination localisation. Then, dense scanning with a high spatial resolution is performed only within the identified delaminated region for delamination visualization. This study especially focuses on the initial delamination localisation using adaptive coarse scanning. Laser ultrasonic responses from two pitch-catch paths, names inspection pairs, are obtained within a specified coarse scanning grid. Then, potential delamination locations within the given grid are estimated through time-of-flight analysis of delamination reflected waves. Once potential delamination locations are estimated, new inspection pairs are placed near the potential locations for precise localisation. These steps are repeated for every coarse scanning grids on the target wind turbine blade. The feasibility of the proposed technique for rapid delamination detection is demonstrated with a 10 kW glass fibre reinforced plastic wind turbine blade.

Vibrational damage detection using fractal surface singularities with noncontact laser measurement

This study concerns damage detection in plate-type structures using fractal surface singularities with noncontact laser measurement of structural dynamic responses. The fractal dimension analysis aided by linear isomorphism is used to deal with mode shapes for a plate with damage. With this method, the linear isomorphism is utilized to remove the local extrema while preserving the damage information of a mode shape, giving a retrofitted mode shape. The retrofitted mode shape is processed by Katz’s fractal dimension analysis to produce a fractal dimension surface with its singular peak indicating the presence and location of the damage. In the method, a series of high-resolution mode shapes of the plate are used, which are acquired by using a noncontact measurement system consisting of a piezoceramic transducer as the actuator and a scanning laser vibrometer as the sensor. The capability of the method to locate and quantify damage is numerically demonstrated using a two-side-clamped aluminum plate with cracks of various depths; the efficacy of the method in identifying complex cracks is experimentally validated using a suspended aluminum plate bearing a cross-like crack. The numerical and experimental results show that the proposed method can accurately identify complex damage in plates, requiring neither benchmark models for the entire structure under investigation, or any prior knowledge of the material properties and the boundary conditions of the structure.

Temperature and damage influence on electromechanical impedance method used for carbon fibre–reinforced polymer panels:

This article deals with damage detection process under varying temperature. Carbon fibre–reinforced polymer samples are investigated using electromechanical impedance method. In the article, influence of changing temperature on resistance in electromechanical impedance is investigated. Authors propose new approach for compensation of temperature influence on damage detection. Damage detection is based on root mean square deviation index. Due to strong damping of utilized composite material, low-frequency range is utilized in this research. Real part of electromechanical impedance is measured for frequency band 1–20u2009kHz. Damage is in the form of artificially made delamination with different sizes. Authors also discuss the problem of influence of structure’s boundary condition on low-frequency measurements. In the research, scanning laser vibrometry for guided wave propagation method is utilized for visualization of the introduced delamination.

Local coordinate systems-based method to analyze high-order modes of n-step Timoshenko beam

High-frequency transverse vibration of stepped beams has attracted increasing attention in various industrial areas. For an n-step Timoshenko beam, the governing differential equations of transverse vibration have been well established in the literature on the basis of assembling classic Timoshenko beam equations for uniform beam segments. However, solving the governing differential equation has not been resolved well to date, manifested by a computational bottleneck: only the first k modes (ku2009≤u200912) are solvable for i-step (iu2009≥u20090) Timoshenko beams. This bottleneck diminishes the completeness of stepped Timoshenko beam theory. To address this problem, this study first reveals the root cause of the bottleneck in solving the governing differential equations for high-order modes, and then creates a sophisticated method, based on local coordinate systems, that can overcome the bottleneck to accomplish high-order mode shapes of an n-step Timoshenko beam. The proposed method uses a set of local coordinate systems in place of the conventional global coordinate system to characterize the transverse vibration of an n-step Timoshenko beam. With the method, the local coordinate systems can simplify the frequency equation for the vibration of an n-step Timoshenko beam, making it possible to obtain high-order modes of the beam. The accuracy, capacity, and efficiency of the method based on local coordinate systems in acquiring high-order modes are corroborated using the well-known exact dynamic stiffness method underpinned by the Wittrick-Williams algorithm as a reference. Removal of the bottlenecks in solving the governing differential equations for high-order modes contributes usefully to the completeness of stepped Timoshenko beam theory.

Non-baseline identification of delamination in plates using wavelet-aided fractal analysis of two-dimensional mode shapes

Delamination is a typical form of damage in composite plates. Identification of delamination in plates has been a focus of increasing research interest in relatively recent years. This study develops a new approach, termed a scale waveform dimension analysis of two-dimensional mode shapes, to identify delamination in composite plates. The scale waveform dimension analysis comprises two components: decomposition of a mode shape into scale mode shapes and waveform dimension analysis of scale mode shapes. The first component acts as a splitter that broadly splits a noisy mode shape into three sets of trend-, noise-, and damage-scale mode shapes, from which the damage scale mode shapes can be selected for use in damage characterization; the second component functions as a detector to detect abnormalities of damage scale mode shapes, to indicate the presence and location of delamination. The efficacy of the method is numerically studied and experimentally examined using composite plates containing small delamination. The results show that the proposed method can identify delamination with great accuracy in noisy conditions, needing no intact baseline mode shapes nor any prior knowledge of either the material properties or boundary conditions of the plate being inspected.