Structural Health Monitoring, Photogrammetry & DIC, Volume 6

In this paper, a modification to Unified Matrix Polynomial Approach (UMPA) for modal parameter identification of mechanical systems is suggested. Following the proposed modification, the measured Frequency Response Functions (FRF)/Impulse Response Functions (IRF) matrices of the system are manipulated so that the vibrational modes of the system can be identified at smaller model orders. A multi degree of freedom numerical case study and the experimental data of a circular plate are then employed to investigate the enhancement in performance of UMPA framework due to the proposed modification. It will be shown that following the proposed data manipulation, matrices with large values of condition number can be avoided in modal parameter estimation.

A presence of a high amplitude periodic signals in the output responses from operating structures often pose a challenge for output-only system identification and, in case of health monitoring, damage detection/localization methods. This paper introduces a pre-processing approach that removes the harmonic part from the output signals directly in the time domain. The new method uses orthogonal projections of the harmonic realization of the signal onto the raw time series within the stochastic subspace framework. Proposed algorithm is tested on two experimental examples. First, an aluminum plate excited with both random white and periodic excitations. Second, a full-scale industrial case of a ferry excited by a random environmental load with harmonic interference from a rotating machinery on-board. In both cases the proposed method removes the harmonics from the structural responses while leaving the random part of the output signal.

Manually identifying mode shapes generated from finite element solvers images is an expensive task. This paper proposes an automated process to identify mode shapes from gray-scale images of compressor blades within a jet-engine. This work introduces mode shape identification using principal component analysis (PCA), similar to approaches in facial and other recognition tasks in computer vision. This technique calculates the projected values of potentially linearly correlated values onto P-linearly orthogonal axes, where P is the number of principal axes that define a subset space. Classification was done using support vector machines (SVM). Using the PCA and SVM algorithm, approximately 5300 training images representative of 16 different modes were used to create a classifier. The classifier achieved on average 98% accuracy when tested using a test set of approximately 2000 images given P = 70. The results suggest that using digital images to perform mode shape identification can be achieved with high accuracy. Potential generalization of this method could be applied to other engineering design and analysis applications.

High-speed camera measurements are increasingly being used in modal analysis to measure full-field response measurements using Digital image correlation and other Optical Flow methods. High-speed cameras can be very expensive, this is why this paper aims at measuring and identifying the full-field response using cheaper still-frame cameras, such as DSLR and mirrorless cameras. Using Spectral Optical Flow Imaging (SOFI) full-field operational shapes can be acquired using still-frame cameras. This study demonstrates a hybrid modal parameter identification of full-field mode shapes using an accelerometer and a DSLR camera, for responses far above the DSLR camera frame-rate (demonstrated up to 1 kHz).

In recent years, high-speed cameras permit to record high-resolution images at several thousand frames-per-second. In addition to this, Digital Image Correlation (DIC) measures full-field displacements and strains in 3D from stereo camera images and perform Operational Deflection Shape and Modal Analysis on the data. Several papers have demonstrated the validity of the approach on laboratory cases, comparing and validating the results with those obtained using more standard measurement techniques (accelerometers, strain gauges, lasers). Very limited cases have been however investigated on the possibility to combine high-speed DIC and standard accelerometer-based measurement to fully exploit the advantages of both techniques. In this paper, the possibility to combine global acceleration measurements on an F16 during a classical Ground Vibration Test with local full-field camera measurement is investigated. The advantages of the combined approach are clear, as the standard measurement will provide the global mode shapes of the aircraft, which can be used for certification and modal validation, while the local high-speed camera measurement system can provide displacement and strain field data with an unmatchable spatial resolution. In particular, the paper will focus on the possibility of using the local displacement measurements to better characterize the non-linear behavior of the connection between the wing and the payload.

Accelerometers have been conventionally used to measure the response of structures for modal analysis. These pointwise sensors only provide information at a few discrete locations being measured. Additionally, the use of accelerometers to capture the response at discrete locations can mass-load the structure. Thus, the obtained results may not predict the true dynamics of the structure. Stereo-photogrammetry and Three-Dimensional Digital Image Correlation (3D DIC) have recently been adopted to collect operating data for vibration analysis. These non-contact optical techniques provide a wealth of distributed data over the entire structure. One of the limitations of a stereo-camera system is its line of sight, which limits the field of view; a single pair of DIC cameras may not be able to provide deformation data for the entire structure. Several pairs of cameras may be coupled simultaneously to perform DIC measurement on large complex structures. However, the use of multiple cameras involves huge costs and may not be a viable choice. In this paper, a multi-view 3D DIC approach is used to predict the dynamic characteristics of a cantilever beam as a sample structure. A pair of DIC cameras is roved over the entire structure to capture the deformation data of each field of view. Each measured data includes the geometry and displacement data which is later mapped into a universal coordinate system. The measured data is stitched in the frequency domain to extract the operating shapes of the entire structure.

Digital Image Correlation (DIC) has proven itself to be a highly versatile and accurate method to measure 2D and 3D displacement, deformation, and strain in a wide range of structures and objects. A major advantage is that it is a non-contact, full-field measurement technique; it measures phenomena across the entire target object without having to attach sensors directly to the object. Despite the ability to measure many static and dynamic phenomena, the cameras and data acquisition equipment are almost exclusively set up in a static configuration. The cameras are often mounted on tripods and remain positioned in the same location while taking measurements. Such an immobile measurement platform prevents DIC from being employed to measure objects in inaccessible locations, such as bridges and tall buildings. An unmanned aerial vehicle carrying digital image correlation cameras has high mobility and can easily access regions on structures that would otherwise be too expensive or dangerous to measure with conventional static camera setups. This paper presents the development and testing of a prototype mobile digital image correlation platform. The resulting platform carries all of the necessary equipment on-board the drone and can be controlled by a single user with a remote control. It is shown that the prototype drone platform is capable of taking accurate and repeatable measurements while airborne. This drone aims to be used for vibration measurement and structural health monitoring of structures such as wind turbines and bridges.

Various identification methods have been introduced in many manners using numerical techniques to validate a complicated structures described in FEM by comparing experimentally measured modal data. The objection of this study is to propose a methodology to identify a perturbed structure by comparing measured modal data to the original FEM data. Identified structures will improve the accuracy to the numerical model by minimizing the differences between those two models. Base-line model will be constructed by using FEM and will be compared to perturbed model by solving inverse problem. Measured modal responses, which are eigenvalues and eigenvectors, will be applied to satisfy the equilibrium and to minimize the differences of modal responses between the original model and the perturbed model. In this study, a neural networks-based detection method using modal properties is presented as a method for the identification which can effectively consider the modeling errors. Also experimental examples will be followed. Due to lack of number of the sensors, DOF-based reduction method is used to restore full model. As neural network is used for identification method, detailed schemes will be reported. In the present study, neural networks-based identification method will be proposed and will be verified by experimental examples. Experimental examples will demonstrate that the proposed method have efficiencies in accuracy of identifying structural model.

In this study, piezo stripe actuators were used to control the vibrations of a flexible cylinder undergoing underwater flow-induced vibrations. The piezo actuators were attached at the anti-nodes of a rectangular plastic beam and urethane rubber was used to mold the test model to have a circular cylinder shape. Forced base oscillation experiments were first carried out in air to characterize the system and piezo responses. Experiments were then performed in a recirculating water channel with the flexible cylinder in a uniform free stream, where the cylinder undergoes self-excitation due to vortex shedding in the wake and forced excitation due to the piezo actuators. The actuators were oriented to apply an excitation only in the in-line direction of the flow. In the tests, two separate cases were investigated. In the first case, the piezo actuators were activated at a flow speed corresponding to a flow-induced response with a spatial mode change, causing the cylinder to be excited with a higher mode, leading to a significantly smaller amplitude response than without the piezo actuation (vibration suppression). In the second case, piezo actuators were activated at a flow speed corresponding to a significant flow-induced amplitude increase. The interaction of the piezo forcing and the forced response of the cylinder results in a jump to the higher amplitude response regime (vibration enhancement). This study presents two important observations: (1) it is possible that piezo actuators can trip the response frequency to force the cylinder to oscillate with a different mode thus reducing the total response amplitude significantly, (2) it is also possible to prematurely increase the response amplitude for a particular flow speed (i.e. jumping from a lower branch to upper branch response).

This study involves the determination of the bending natural frequencies of beams composed by stacked cells of different materials. The focus is on cases with two cells. The analytical model is based on Euler-Bernoulli theory with the variations from one cell to another modeled via logistic functions. This approach leads to a single differential equation with variable coefficients, which is solved numerically using MAPLE®‘s differential equation solvers. A forced motion method is used. Forcing frequencies are changed until large motions and sign changes are observed, leading to the resonant frequencies. Of interest is the validation of the analytically obtained frequencies via experimental results. Here, an experiment is set in which a simple two-cell beam is analyzed, via modal analysis, in order to verify the analytically calculated frequencies. The beam is excited using an impact hammer and the response is recorded using accelerometers. Mode shapes are also obtained via digital image correlation. The beam, including distinct materials, is composed of one cell made of steel and another made of aluminum. The joining method is discussed and results for fixed-free beams are obtained.

Mechanical amplifiers are employed to enhance output displacement of piezoelectric actuators. Dynamic behavior of such an amplified piezoelectric actuator needs to be known accurately in order to verify its suitability for the driven system. The objective of this study is to present a theoretical approach to determine a mathematical model for an amplified piezoelectric actuator (APA) which consists of a stacked piezoelectric actuator (SPA) with rhombus type mechanical amplifier (RPA). Dynamics of the mechanical amplifier is formulated based on distributed-parameter system approach, and Hamilton’s principle is used to obtain a reduced order model. The SPA is then dynamically coupled with the reduced order model of a flexural amplifier by employing the constitutive relations between two substructures. The responses of the coupled system are calculated using linear vibration analysis under harmonic voltage input. Finally, the validity of the developed mathematical model is verified by comparing the calculated velocities with that of finite element solutions and experimental measurements in the frequency domain. The finite element (FE) solution is obtained using ANSYS software. Output velocity of the sample RPA is measured with the aid of a laser vibrometer. It is observed that the results obtained from the mathematical model show a very good agreement with those of the finite element analysis and test measurements.

Structural dynamics identification is an important part of both the design and certification process for large-scale structures and specifically utility-scale wind turbine blades. Finding the correspondence between the estimated natural frequencies and the mode shapes of interest can be a very challenging due to the sheer size of the structures and the large amount of instrumentation required. The state of the art methods in experimental modal analysis (EMA) and operational modal analysis (OMA) require attachment of numerous accelerometers along the test structure to extract the natural frequencies and the mode shapes. Instrumenting large structures with accelerometers and handling the wiring and the connections can be a very labor-intensive task; therefore, alternative methods should be considered to address this problem. Within this paper, the capabilities of phase-based video magnification and motion estimation are investigated to find the correspondence between the natural frequencies and the mode shapes. The sequence of images (video) is recorded from the vibrating wind turbine blade and then processed using the phase based motion estimation to extract the spectrum of the response of the wind turbine blade to the impact excitation. Afterward based on the obtained spectrum the recorded videos are magnified to visualize the operating deflection shapes. The motion magnified videos represent the visual perception of the operating deflection shapes, which can be used to find the correspondence between the natural frequencies and the mode shapes. The results of this method have also been validated using the benchmark modal data from the accelerometers as well as the point tracking optical measurement method.

Damping of vibrating systems converts the vibrational energy into other forms, such as heat and sound radiation. Heating of the material is often assumed to be one of the biggest drains of energy; however, it is very hard to experimentally identify how much of the damped energy is converted to heat. This manuscript introduces the damping heat coefficient and via high-speed cameras (optical and thermal) identifies that, for the selected material, approximatelly 30% of the damped energy is converted to heat.

NC-Checker is a software tool used for monitoring and validating the geometric performance in modern machining centres. Threshold settings allow the Manufacturing or Maintenance Engineer to customise the tool based on specific job or industry tolerance requirements. In order to perform effective long-term monitoring, this has the potential to skew the perceived health state of the machining centre as presented in the NC-Checker benchmark reports. This study brings attention to this fact and its relevance in the pursuit of enhanced levels of automation for geometric performance monitoring tools, in preparation for the machine shop’s transition to Industry 4.0. A sense-check function is proposed to identify unusual alterations based on historical data, utilising a support vector machine methodology to develop a predictive classifier. The models achieved predictive accuracy scores of 87.5% during validation, acquisition of a suitable testing set is under way and the predictive models will be evaluated upon completion.

Real world structures, such as bridges and skyscrapers, are often subjected to dynamic loading and changing environments. It seems prudent to measure high resolution vibration data, in order to perform accurate damage detection and to validate and update the models and knowledge about the operating structure (aka finite element models). Many existing vibration measurement methods could be either low resolution (e.g., accelerometers or strain gauges), and time and labor consuming to deploy in field (e.g., laser interferometry). Previous work by Yang et al. has shown that low-cost regular digital video cameras enhanced by advanced computer vision and machine learning algorithms can extract very high resolution dynamic information about the structure and perform damage detection at novel scales in an relatively efficient and unsupervised manner. More interestingly this work used a machine learning pipeline that made minimal assumptions about lighting conditions or the nature of the structure in order to perform modal decomposition. The technique is currently limited to two dimensions if only one digital video camera is used. This paper uses light field imagers - a new camera system that captures the direction light entered the camera - to make depth measurements of scenes and extend the modal analysis technique proposed in Yang et al. to three dimensions. The new method is verified experimentally on vibrating cantilever beams with out of plane vibration, whose full-field modal parameters are extracted from the light field measurements. The experimental results are discussed and some limitations are pointed out for future work.

Safe and reliable operation of hypersonic aircraft, space structures, advanced weapon systems, and other high-rate dynamic systems depends on advances in state estimators and damage detection algorithms. High-rate dynamic systems have rapidly changing input forces, rate-dependent and time-varying structural parameters, and uncertainties in material and structural properties. While current structural health monitoring (SHM) techniques can assess damage on the order of seconds to minutes, complex high-rate structures require SHM methods that detect, locate, and quantify damage or changes in the structure’s configuration on the microsecond timescale.

This paper discusses the importance of microsecond structural health monitoring (μSHM) and some of the challenges that occur in development and implementation. Two model-based parameter estimators are examined for estimating the states and parameters of an example time-varying system consisting of a two degree of freedom system with a sudden change in a stiffness value that simulates structural damage. The ability of these estimators to track this stiffness change, the role of measurement noise, and the need for persistent excitation are examined.

This work uses probabilistic robustness techniques to show how the stability margin of an uncertain controlled structure that operates in a harsh, potentially radioactive environment can be analyzed in order to find a less conservative destabilizing uncertainty perturbation. The uncertainty is quantified in terms of a measure on the size of the covariance matrix in a multivariate Gaussian distribution. This uncertainty is used to capture the aggregate effects on a structure’s dynamic behavior due to material changes resulting from radiation embrittlement and mechanical fatigue. A probabilistic-robust full-state feedback \({\mathcal {H}_\infty }\) controller is synthesized for a low-dimensional structural model using a technique known as scenario-based probabilistic-robust synthesis. A probabilistic-robust stability margin is defined and extracted from a stability degradation function, demonstrating that a fourfold increase in the amount of uncertainty in the model can be tolerated if the designer is willing to concede a small probability that the actively-controlled structure may be unstable for certain system configurations.

A practical procedure of implementing shape sensors for full-field deformation sensing of a structure is demonstrated in this extended abstract. The sensors are constructed using a piezoelectric film material which is bonded to the surface of a beam structure. The electrical outputs of the sensors are then calibrated such that the modal coordinates of the beam displacement can be measured. Calibration of the sensors is performed by using beam displacement data from high-speed 3D digital image correlation (DIC). Operational modal analysis is used to estimate mode shapes and to extract the modal coordinates from the DIC data. The shape sensor is then implemented by calibrating sensor voltages to the extracted modal coordinates. This extended abstract presents the procedure and results of this methodology on a beam instrumented with rectangular piezoelectric sensors of arbitrary length.

Model selection is a challenging problem that is of importance in many branches of the sciences and engineering, particularly in structural dynamics. By definition, it is intended to select the most plausible model among a set of competing models, that best matches the dynamic behaviour of a real structure and better predicts the measured data. The Bayesian approach is based essentially on the evaluation of a likelihood function and is arguably the most popular approach. However, in some circumstances, the likelihood function is intractable or not available even in a closed form. To overcome this issue, likelihood-free or approximate Bayesian computation (ABC) algorithms have been introduced in the literature, which relax the need of an explicit likelihood function to measure the degree of similarity between model prediction and measurements. One major issue with the ABC algorithms in general is the low acceptance rate which is actually a common problem with the traditional Bayesian methods. To overcome this shortcoming and alleviate the computational burden, a new variant of the ABC algorithm based on an ellipsoidal nested sampling technique is introduced in this paper. It has been called ABC-NS. This paper will demonstrate how the new algorithm promises drastic speedups and provides good estimates of the unknown parameters. To demonstrate its practical applicability, two illustrative examples are considered. Firstly, the efficiency of the novel algorithm to deal with parameter estimation is demonstrated using a moving average process based on synthetic measurements. Secondly, a real structure called the VTT benchmark, which consists of a wire rope isolators mounted between a load mass and a base mass, is used to further assess the performance of the algorithm in solving the model selection issue.

A valuable solution for structural vibration control of lightly damped systems, subjected to random disturbance, is to provide active damping by generating a control force proportional to the local velocity of the structure. It has been shown in the literature that an optimal feedback gain exists, at which the kinetic energy of the structure is minimised. Furthermore, other studies have shown that the minimisation of the kinetic energy can be approximated with the maximisation of the power absorbed by the control unit, reducing the amount of information required for the estimation of the performance of the control system. In this paper the reduction of flexural vibration on a plate by means of a local velocity feedback control, with a collocated inertial actuator and sensor pair, is considered. The performance of the control unit is investigated both numerically and experimentally, in terms of the kinetic energy of the structure and the power absorbed by the control unit. The influence of the frequency range considered in the assessment of the performance is analysed. In particular, the equivalence between the minimisation of the kinetic energy and the maximisation of the power absorbed is investigated, as a crucial step into the design of a self-contained locally tunable control unit.

This research consists of theoretical and experimental studies of a stroke limited inertial, or proof mass, actuator used in active vibration control. Traditionally, inertial actuators are used with velocity feedback controllers to reduce structural vibrations. However, physical limits, such as stroke saturation, can affect the behaviour and the stability of the control system. In fact, stroke saturation results in impulse like excitations, which are transmitted to the structure that is liable to damage. Moreover, the shocks produced by the impacts are in phase with the velocity of the structure. This produces an input force, which reduces the overall damping and eventually leads to limit cycle oscillations and the instability of the system. This paper examines the experimental implementation of a nonlinear feedback controller to avoid collisions of the proof mass with the actuator’s end stops, hence preventing the instability of the system due to stroke saturation. Firstly, the nonlinear behaviour of the stroke limited inertial actuator is reported. This allows identifying the stroke length of the proof mass. Secondly, the nonlinear feedback controller is presented, which acts as a second loop alongside the velocity feedback control loop. The main purpose of the nonlinear feedback controller is to increase the damping of the actuator when the poof mass gets close to the end stops. Finally, the experimental implementation of the nonlinear controller is investigated and a comparison in terms of performance and stability of the control system is made when both the feedback loops or only the velocity feedback loop are present.

The human auditory mechanism can detect sound frequencies ranging from 20 Hz to 20 kHz, over a broad pressure range of 0–120 dB SPL due to its nonlinear amplification performed by the cochlea. Sound waves travel through the ear canal, eardrum and the three bones of the middle ear. The last bone of the middle ear (stapes) pushes on the oval window and creates propagating waves in the cochlea. Each of the sound frequency components excites a specific location along the basilar membrane when it travels through the cochlea. These are then coupled to the hair cells, which apply their nonlinear compressibility and amplification behavior to improve sound detection. These functions of the cochlea are the inspiration to design more sensitive and capable sensors.

The primary objective of this work is to mimic the nonlinear amplification of cochlea by developing piezoelectric based active artificial hair cells (AHCs). By examining models of the biological cochlea, a nonlinear feedback control law is designed which applies the appropriate forcing conditions to the beam to amplify or suppress vibrations initially induced by an external stimulus. To achieve this goal, a two degree of freedom model of the AHCs is created. Control laws are then applied to the system to mimic the phenomenological active nonlinear functions of the outer hair cells seen in the mammalian cochlea and to improve the ability of a single AHC to work for more than one frequency.

Impulsive forces cause sudden variations in dynamic systems and may result in fatal damage to the system especially in turbines where the whole system is enclosed inside a casing with very small clearance between the blades and the casing. Electromagnetic actuators have been known to apply non-contact electromagnetic force on a rotor- shaft section preventing rotor-shaft vibrations. This work attempts to investigate the comparison of two different control laws in controlling the vibrations caused by noises such as sudden flow rate change, blade loss, or excitations occurring due to seismic vibrations. A rotor-shaft system is developed within a simulation framework which includes an actuator placed away from the bearings. Literature shows the use of conventional PD (Proportional Derivative) control law which is equivalent to a 2-element support model. This work novels the 3-element viscoelastic support model, which is found to offer better vibration mitigation abilities in terms of controlling transient excitations. Preliminary theoretical simulation using linearized expression of electromagnetic force and the accompanying example show good reduction in transverse response amplitude, postponement of instability caused by viscous form of rotor internal damping.

Vibration reduction is a significant problem in the design and construction of vehicle suspensions (Lozia and Zdanowicz, IOP Conf Ser Mater Sci Eng 148:12014, 2016; Konieczny et al., J Low Freq Noise Vib Act Control 32:81–98, 2013). Passive semi-active and active methods are used in order to reduce vibrations. Considerations related to active and semi-active vibration reduction and the influence of disturbances on such objects can be found in many publications. In the case of these systems, the aim is always to find a compromise between their efficiency and energy consumption. The control law for such systems is usually determined as a solution to the optimisation problem with quadrant quality indicator. Energy limitation is taken into account by selection coefficients of the weighting matrix associated with the control signals vector. The efficiency of vibration reduction is able to be improved in the entire useful frequency range of the system operation but this generally results in an increase in the demand for external energy. An additional problem in the case of vehicle suspensions includes the need for increased vibration reduction for selected frequencies. This is related to the internal vibration frequencies of the driver’s internal organs. The paper presents the synthesis of a weighted multitone optimal controller (WMOC) for an active vibration reduction system. The control signal in this case is determined on the basis of the identified sinusoidal disturbances vector. The vibration transmissibility function and the energetic indicators for the active suspension were determined while taking note of nonlinearities occurring in the actual vehicle. The analysis of energy indicators (e.g. energy, maximum power) is presented, depending on the level of vibration reduction efficiency. The results were compared with analogous linear-quadratic regulator (LQR).

In many designs of vehicle suspension anti-roll bars are used for body roll reduction (Cronjé and Els, J Terramechanics 47:179–189, 2010; Her et al., IFAC Proc. 2013. https://​doi.​org/​10.​3182/​20130904-4-JP-2042.​00152). Such solutions are used in compact cars (C-segment), mid-size cars (D-segment), mid-size luxury car (E-segment) and even sports cars (S-segment). Antiroll bars are torsion bars connecting both sides of car suspension and they are connected with suspension arms. When car wheels move in vertical direction these torsion bars are twisted. Increasing torsional stiffness of front or rear suspension is the main role of sway bars. The use of these rods reduces tilting of the body while riding at high speed when the tilt of a car body is caused by the centrifugal force acting on the car. This force compress suspension spring with one side of the car, and extends on the other. The torque generated by the torsion bars reduce the difference in springs suspension. It reduces the compression of springs on one side of a car and extension on the other. Reduction of car body tilt improving handling and road holding and therefore improve safety. Antiroll bars also allow for the reduction of lateral vibrations caused by road roughness. During straight driving on equal road surface or under the same excitation of the wheels, the stabilizer doesn’t work. During overcoming high road irregularities, the force acting on one of a wheel is transferred to the other via the bar. Antiroll bars also allow for the reduction of lateral vibrations caused by road inequalities. This causes unwanted oscillations. This effect is more noticeable if angle stiffness of the stabilizer is higher. In order to avoid such phenomena, active anti-roll bars are used. The most commonly used solutions are two-part active disconnect anti-roll bar or just active antiroll bar. In case of a two-part disconnectable anti-roll bar a hydraulic actuator connected to the ends of the roll bars usually is used. In such case, wheels work independently of each other so that the reactions from one wheel are not transferred to the other. If necessary, the stabilizer is connected by means of an actuator and works just like the classic one. In an active stabilizer a hydraulic actuator connected to the ends of the antiroll rods usually is used. Controlling the pressure or flow rates of the oil gives wide possibilities for acting actively on the anti-swaying of the vehicle.