Strain Mode Shapes Research Articles

Structural damage identification through variations in modal quantities using modal strain energy and mode shape curvature methods

Structural damage identification through variations in modal quantities using modal strain energy and mode shape curvature methods

Strain mode measurement of asphalt pavements using distributed fibre optic sensor data

This paper proposes a method for measuring strain modes in asphalt pavements using distributed fibre optic strain sensor data. A processing algorithm based on cross power spectral density (CPSD) was developed to utilize high spatial resolution strain data to determine the CPSD peak frequency and corresponding relative amplitude. The proposed method was applied in both laboratory and field settings, comparing the results of distributed fibre optic cables with those of accelerometers or theoretical solutions to validate accuracy. Local heating of asphalt structures was used to test the sensitivity of the measured strain modes to changes in material properties. The results demonstrate that different fibre optic cables can provide peak frequencies comparable to traditional accelerometers (±0.6 Hz). Additionally, they offer relative amplitude with a resolution of 1 cm, achieving a modal assurance criterion exceeding 0.95 when compared to theoretical strain mode shapes. The method also sensitively reflects material property changes at different positions within the asphalt structure. This indicates that the proposed approach can effectively measure strain modes in asphalt structures, offering a more detailed understanding of the distribution of structural properties compared to traditional methods.

Finite element model updating and damage detection using strain-based modal data in the Bayesian framework

This paper proposes a novel methodology for Bayesian model updating and damage detection of a structural system using strain-based modal data. The strain-based modal data are assumed to consist of the posterior statistics of natural frequencies and strain mode shapes corresponding to measured strains from a classically damped system. The dynamic strain-based equation of the motion is formulated utilizing the energy functional of the structural system and the strain displacement relation. The state variables in the considered strain-based formulation consist of the strains and the elemental rigid body displacements. The methodology is developed by incorporating strain-based formulation into the Bayesian framework for Finite Element (FE) model updating. Besides, additional uncertain parameters in the form of system strain-based modal parameters are introduced in the eigenvalue equation to avoid mode-matching. The model reduction technique is utilized to eliminate the rigid body displacements and the strains that are not measured. Metropolis-Hastings (MH) within Gibbs sampling is proposed to simulate samples from the posterior Probability Density Function (PDF) of the model parameters of the FE model. The effectiveness of the proposed methodology is demonstrated using simulated examples. An experimental study is also conducted to validate the proposed methodology.

Single-Shot Time-Averaged Shearography for Vibration Strain Mode Shape Visualization

Single-Shot Time-Averaged Shearography for Vibration Strain Mode Shape Visualization

Vibration monitoring and acoustic emission sensing during progressive load tests of corroded reinforced concrete beams

Corrosion of reinforcement in concrete civil structures poses a significant challenge to their integrity and durability. To ensure the safety and longevity of such structures, effective monitoring strategies that can accurately detect, localise and assess the progression of damage are crucial. For most existing concrete structures, this is often challenging, as damage is already present when the monitoring campaign starts. In addition, reinforced concrete structures can be subject to a combination (or a succession) of corrosion and load-induced damage. By combining multiple measurement techniques, a more accurate and reliable condition assessment of concrete civil structures can be aimed for. This paper presents a comprehensive experimental study of the combination of vibration-based monitoring (VBM) and acoustic emission (AE) sensing techniques during progressive load tests of corroded reinforced concrete beams. Five beams were subjected to a cyclic four-point bending test, three of which were previously corroded while two beams remained undamaged prior to the mechanical loading. The influence of pre-existing corrosion damage and corresponding longitudinal concrete cracking on the modal characteristics (natural frequencies and strain mode shapes) and AE outcomes is investigated during the four-point bending test. The monitoring results obtained by both techniques are shown to be influenced by the pre-existing longitudinal concrete cracking caused by the reinforcement corrosion. Lower AE activity and a lower reduction in natural frequencies is observed for corroded RC beams during load bending tests when compared to uncorroded specimens. In addition, bending cracks occurring within the corroded zones appear to have a very limited effect on the identified strain mode shapes. These observations could possibly result in an underestimation of the damage and corresponding overestimation of the load-carrying capacity, as the corrosion damage conceals the occurrence of bending cracking on the AE and VBM outcomes.

Blade Strain Peak Localization Method With Single Transducer During Multimode Vibration

Abstract The dynamic strain/stress measurement of blades provides an effective method to anticipate fatigue life and investigate of failure causes. Unlike the blade strain peak is fixed during singlemode, which can be measured by a single transducer, the strain peak distribution changes over time and space during multimode vibration situations. The existing method reconstructs the full-field strain to find the peak point with multiple transducers. In this work, a single transducer-based full-field dynamic strain reconstruction technique is presented to find the strain peak position on rotor blades. First, the mode response is obtained by separating the measured response from a single strain gauge based on Ensemble Empirical Mode Decomposition. Second, based on the strain mode shape from the finite element model, the reconstructed strain transmissibility matrix is created between a single measured location and the full field. Third, the dynamic strain of the blade can be reconstructed at any location and time by combining the separated mode response with the RST matrix. Finally, the strain peak localization is identified according to the distribution of full-field dynamic strain during multimode vibration. The above process is verified by experimental data from rotor blades with the maximum error of reconstructed strain below 12% and three explicitly recognized strain peak positions.

Quantification of Statistical Error in the Estimate of Strain Power Spectral Density Transmissibility for Operational Strain Modal Analysis

The use of strain modes in structural health monitoring has been constantly increasing because of their superior sensitivity to local structural anomalies. This study aims to investigate the applicability and robustness of power spectral density transmissibility (PSDT) in operational strain modal analysis (OSMA). By noting that OSMA in the frequency domain is vulnerable to the error of spectral estimates, uncertainty quantification stemming from strain spectral estimates and the error propagation analysis in OSMA are conducted from an analytical perspective. The main contributions include the following: (i) the mean and variance of strain PSDT estimates are asymptotically derived based on statistical moment theory and the statistics of PSD estimate error, (ii) the coefficients of variation (c.o.v.) of the strain PSDT estimate and strain spectral estimates are compared with each other through asymptotic analysis to elaborate the robustness of strain PSDT, and (iii) the variability of the strain mode shape is quantified based on the asymptotic formula of strain PSDT estimates tending to local minima of asymptotic zero variance at the resonances. The accuracy and efficiency of the quantification and propagation analysis are validated through numerical and experimental test data accompanied by various parametric studies.

Strain experimental modal analysis of an Euler–Bernoulli beam based on the thermoelastic principle

The strain mode shapes can be utilized as an indicator of vibration fatigue-hotspots and are utilized for predicting the distribution of damage intensity. However, the conventional approach for measurement, which involves using strain sensors, does not offer the necessary high spatial density required for accurately identifying critical locations or creating a comprehensive map of damage intensity. Non-contact methods have been employed to indirectly determine the full-field strain shapes, but when measuring kinematic quantities, a relation between kinematics and stress/strain must be known. For Euler–Bernoulli beam, the double spatial derivative is required which introduces a significant uncertainty. In contrast, by leveraging the thermoelastic principle, the full-field stress/strain response of an arbitrary structure can be directly measured using a high-speed infrared (IR) camera. The thermoelastic principle has not been extensively researched for strain experimental modal analysis (EMA). In this study, the hybrid EMA (based on one high-dynamic range sensor) was researched for thermoelastic identification of an Euler–Bernoulli beam. The minimum stress/temperature variation required to achieve accuracy comparable to scanning-laser kinematics-based strain mode shapes was investigated. The findings demonstrate that even when the noise floor is significantly higher than the signal, full-field strain mode shapes can be identified using IR cameras and the hybrid EMA method. By considering the minimum stress/temperature variation determined in this research (for aluminum and steel), the accuracy of thermoelasticity-based strain shapes can be evaluated during the experiment-design stage. While this research is theoretically and experimentally based on Euler–Bernoulli beam, generalization of the thermoelastic principle to arbitrary structure is feasible.

Experimental study on acoustic emission sensing and vibration monitoring of corroding reinforced concrete beams

Reinforcement corrosion is a major issue in reinforced concrete structures with severe societal and economic consequences if not detected and treated in time. This paper presents an elaborate experimental study to effectively monitor chloride-induced corrosion damage in reinforced concrete beams. A combined method of acoustic emission sensing and vibration-based monitoring is developed to detect, characterise and localise damage. Additionally, crack measurements on the concrete surface are performed as a reference technique. Four beams are corroded with an accelerated corrosion set-up while two additional beams are used as reference specimens. Whereas these monitoring techniques have already been applied individually to assess corrosion in reinforced concrete beams, they are here combined, in order to verify their complementarity. This results in an elaborate and innovative data-set which allows us to draw new conclusions on the way the techniques provide information on the evolution of corrosion damage in time and space. It was found that acoustic emission sensing can accurately detect and localise damage before cracking of the concrete, especially after dedicated noise filtering through clustering of the AE signals. Vibration-based monitoring is less sensitive to early damage, yet natural frequencies contain absolute information about the stiffness decrease due to corrosion damage, and strain mode shapes can localise damage on a larger scale. In addition, results from both techniques are in line with the crack measurements. As a result, the combination of these various monitoring methods offers valuable and complementary insights about the corrosion process.

Turning Telecommunication Fiber-Optic Cables into Distributed Acoustic Sensors for Vibration-Based Bridge Health Monitoring

We introduce a nondedicated bridge health monitoring (BHM) system that turns pre-existing telecommunication fiber-optic cables into distributed acoustic sensors to collect bridge dynamic strain responses. Due to extensively installed telecommunication fiber cables in the cities, our telecommunication cable-based system enables efficient and low-cost BHM without the requirement of on-site sensor installation and maintenance; however, it is challenging to extract bridge damage-sensitive information (e.g., natural frequencies and mode shapes) from this nondedicated strain data as it has large measurement noise and error propagation. To overcome the challenge, we develop a physics-guided system identification method that models strain mode shapes based on physics-guided parametric mode shape functions derived from bridge dynamics. We then estimate the displacement mode shape function by analytically double-integrating the modeled strain mode shape. Our method improves the accuracy of estimating bridge damage-sensitive features and reduces error propagation by constraining strain and displacement mode shapes with bridge dynamics. We evaluated our system on a concrete continuous three-span bridge in San Jose, California. Our system successfully identified the first three natural frequencies and reconstructed strain and displacement mode shapes in a meter-scale resolution.

An Optimal Strain Gauge Layout Design for the Measurement of Truss Structures

Sensor measurements diagnose and evaluate the structural health state. A sensor configuration with a limited number of sensors must be designed to monitor sufficient information about the structural health state. The diagnosis of a truss structure composed of axial members can begin with a measurement by the strain gauges attached to the truss members or by the accelerometers and displacement sensors at the nodes. This study considered the layout design of the displacement sensors at the nodes for the truss structure by using the effective independence (EI) method based on the mode shapes. The validity of the optimal sensor placement (OSP) methods depending on their synthesis with the Guyan method was investigated by the mode shape's data expansion. The Guyan reduction technique rarely affected the final sensor design. A modified EI algorithm based on the strain mode shape of the truss members was presented. A numerical example was analyzed, showing that the sensor placements were affected depending on the displacement sensors and strain gauges. Numerical examples illustrated that the strain-based EI method without the Guyan reduction method has the advantage of reducing the number of sensors and providing more data related with the displacements at the nodes. The measurement sensor should be selected when considering structural behavior, as it is crucial.

Electrode Design Based on Strain Mode Shapes for Configurable PMUTs

Electrode Design Based on Strain Mode Shapes for Configurable PMUTs

A Feature of Mechanics-Driven Statistical Moments of Wavelet Transform-Processed Dynamic Responses for Damage Detection in Beam-Type Structures

Multiple damage detection using structural responses only is a problem unresolved that is in the field of structural health monitoring. To address this problem, a novel feature of mechanics-driven statistical moments of wavelet transform-processed dynamic responses is proposed for multi-damage identification in beam-type structures. This feature is referred to as a continuous wavelet transform (CWT)-second-order strain statistical moment (SSSM), with CWT-SSSM in the abbreviation. The mechanical connotation of CWT-SSSM lies in that the SSSM of each order principal vibration contains strain mode shapes, inducing greater sensitivity to local damage. With this method, the CWT is used to extract and amplify the singularities caused by damage in each order SSSM curve, following which the data fusion technology and three-sigma rule in statistics are adopted to construct the damage index. The presence of damage is characterized by the abrupt change in the damage index. The soundness and characteristics of the CWT-SSSM feature are verified by identifying multiple damages in a cantilever beam bearing two breathing cracks. The results show that the proposed feature can accurately designate multiple cracks free of baseline information on the intact counterpart; moreover, it has robustness against noise and applicability under excitations of approximately uniform spectra.

Influence of frost and local stiffness variations on the strain mode shapes of a steel arch bridge

Natural frequencies are probably the most widely used modal characteristics in vibration-based monitoring. However, they can be highly influenced by temperature and this influence can completely mask the effect of even severe damage. This translates into a necessity for time-consuming data-normalization techniques to remove the influence of temperature and identify damage. Displacement mode shapes of homogeneous material structures are less influenced by temperature, but obtaining them in a dense grid, which is required for damage localization, is cumbersome due to the large number of sensors needed. Strain mode shapes on the other hand can be insensitive to temperature variations, while obtaining them in a dense grid is possible when fiber-optic sensors such as fiber-Bragg gratings (FBG) are used. This work presents the results of the continuous monitoring of a steel railway bridge for a period of almost two years, where modal data were collected for a wide temperature range. The bridge is instrumented with eighty FBG strain sensors, multiplexed in four fibers. The natural frequencies and strain mode shapes of ten modes have been automatically identified from operational strain time histories, on an hourly basis. A clear influence of temperature on the natural frequency of most modes is identified, especially during frost periods. On the contrary, the strain mode shapes are mostly insensitive to temperature changes and only these of some higher-order modes are slightly and uniformly influenced when frost occurs. This behavior is confirmed also by a finite element model (FE) of the bridge. Furthermore, the FE model is used to investigate the influence of local stiffness changes on the modal characteristics. A clear and local change of the modal strain amplitude is observed at the location of the reduced stiffness, especially when information from all modes is combined in a sensitive damage index.

A Two-Stage Approach for Damage Diagnosis of Structures Based on a Fully Distributed Strain Mode under Multigain Feedback Control

The application of distributed fiber sensing technology in civil engineering has been developed to obtain more accurate and reliable information for structural health monitoring (SHM). With this sensing technique, high-density strain data are provided to benefit the stability and robustness in a closed-loop damage detection method which has not yet been investigated. To address this concern, a two-stage approach for structural damage detection combining a modal strain energy-based index (MSEBI) method with a hybrid artificial neural network (ANN) and particle swarm optimization (PSO) algorithm is proposed. In this study, the fully distributed strain measurement is taken advantage of, and a strain-based, closed-loop system with multiple gains aggregated for damage sensitivity enhancement is established, by which high-precision damage location and quantification can be realized through the proposed two-stage method. For the first step, the closed-loop strain mode shapes are used to construct the MSEBI for damage localization. For the second step, we adopt the PSO algorithm to train the parameters (weights and biases) of the neural network in order to reduce the difference between the real and expected outputs and then use the trained network for quantifying the damage extent. Furthermore, validation is completed by contemplating a two-span, bridge-like structure.

Optimal Sensor Placement for Modal-Based Health Monitoring of a Composite Structure.

Optimal sensor placement is one of the important issues in monitoring the condition of structures, which has a major influence on monitoring system performance and cost. Due to this, it is still an open problem to find a compromise between these two parameters. In this study, the problem of optimal sensor placement was investigated for a composite plate with simulated internal damage. To solve this problem, different sensor placement methods with different constraint variants were applied. The advantage of the proposed approach is that information for sensor placement was used only from the structure’s healthy state. The results of the calculations according to sensor placement methods were subsets of possible sensor network candidates, which were evaluated using the aggregation of different metrics. The evaluation of selected sensor networks was performed and validated using machine learning techniques and visualized appropriately. Using the proposed approach, it was possible to precisely detect damage based on a limited number of strain sensors and mode shapes taken into consideration, which leads to efficient structural health monitoring with resource savings both in costs and computational time and complexity.

Nondestructive evaluation of carbon-fiber composites using digital image correlation, acoustic emission, and optical based modal analysis

Composite materials are increasingly used in the wind industries. Damage detection and health monitoring of composite materials are challenging due to the complex internal structure and unique material properties. Digital image correlation (DIC) and acoustic emission (AE) are both used for damage detection in structures. In this work, DIC performs a full-field strain measurement on the surface of the carbon-fiber specimen while AE continuously monitors and records the AE signals generated from specimen subsurface structure failures. These health monitoring techniques are integrated and evaluated in this study to correlate surface strain measurements and acoustic emission measurements on carbon-fiber specimens. The AE measurement results show that there is a correlation between the occurrence of AE events and the timing of complete specimen failure. DIC with a high-speed stereo camera system is also adopted to extract the change in the resonance frequencies and displacement and strain mode shapes of the specimen during experiments in cyclic loading.

Vibration-based monitoring of an FRP footbridge with embedded fiber-Bragg gratings: Influence of temperature vs. damage

An attractive feature of FRP structures is that Fiber-Optic Sensors (FOS) can be naturally embedded during the production process and provide important structural information immediately after construction. Thus, FOS became very useful also for Vibration-Based Monitoring (VBM) applications. In VBM, damage can be identified by detecting damage-related changes in the modal characteristics of a structure, such as natural frequencies and strain mode shapes. However, natural frequencies can exhibit a low sensitivity to certain types of damage, especially when compared to their sensitivity to temperature. Strain mode shapes though have been proved to be more sensitive to local damage and less to temperature than natural frequencies. In this work, an FRP footbridge is subjected to periodic annual VBM. The dynamic strains of the bridge are monitored with embedded Fiber-optic Bragg Gratings (FBG), a type of FOS that allows determining natural frequencies and strain mode shapes accurately from low-amplitude strain data. Vibration modes are identified from the dynamic strains and the influence of temperature and heavy loading is investigated. The identified modes are used for calibrating a finite element model. Possible damage scenarios on FRP structures are simulated and their influence on modal characteristics is investigated and compared to this of temperature.

A data fusion based diagnostic methodology for in-situ debonding detection in beam-like honeycomb sandwich structures with fiber Bragg grating sensors

The integrity of interfacial bonding in honeycomb sandwich should be diagnosed on regular basis. This paper develops a novel approach to diagnose debonding defects only employing strain measurements under ambient excitations. As debonding defects vary dynamics of the structure, the change ratio of strain modes is promising to indicate the defects. To address diagnostic errors caused by noises, a novel damage index is proposed based on Dempster–Shafer evidence theory, which works out a reasonable global decision from different orders of noisy strain mode shapes. Those modes are estimated by operational modal analysis motivating by the concept of rational fraction polynomial and transmissibility, which reduces the number of input condition and output fitting to single one. Fiber Bragg gratings are employed to capture the structural responses that can deploy as dense sensing nodes. As proof-of-concept testing, the proposed methodology is applied to a honeycomb sandwich beam with seeded debonding defects.

Deflection estimation of beam structures based on the measured strain mode shape

Deflection is of great significance for evaluating the safety performance of long-span bridges, while it is difficult or expensive to be directly measured in actual projects despite numerous displacement sensors have been developed. This paper proposes a displacement reconstruction framework to obtain the dynamic deflection of beam structures using strain data. The framework defines the judgment criteria of curvature symbols and standard side first, and then stochastic subspace identification algorithm is used to calculate the strain mode shapes involved in the vibration, which solves the unclear calculation process and the need for considerable measurement points of the traditional mode superposition method. Furthermore, the displacement mode shapes and corresponding modal coordinates are obtained, and then the dynamic deflections are derived. Numerical simulations of cantilever and simply supported beams illustrate the effectiveness of the proposed framework, and the results show that the error is only 0.69% with only four strain measurement points. The two corresponding model experiments have also been carried out, and the results demonstrate that the deflection estimation error is only 0.14% with five measurement points, which further proves that the developed displacement reconstruction framework can accurately reconstruct the dynamic deflection of the beam structures.