Linear regression quantifies the linear relationship between paired sets of input and output observations. The well known least-squares regression optimizes the performance criterion defined by the residual error, but is highly sensitive to uncertainties or perturbations in the observations. Robust least-squares algorithms have been developed to optimize the worst case performance for a given limit on the level of uncertainty, but they are applicable only when that limit is known. Herein, we present a robust-satisficing approach that maximizes the robustness to uncertainties in the observations, while satisficing a critical sub-optimal level of performance. The method emphasizes the trade-off between performance and robustness, which are inversely correlated. To resolve the resulting trade-off we introduce a new criterion, which assesses the consistency between the observations and the linear model. The proposed criterion determines a unique robust-satisficing regression and reveals the underlying level of uncertainty in the observations with only weak assumptions. These algorithms are demonstrated for the challenging application of linear regression to neural decoding for brain-machine interfaces. The model-consistent robust-satisfying regression provides superior performance for new observations under both similar and different conditions.
The dynamics of three different cutting regimes were compared using the bicoherence estimates. For two regimes corresponding to cutting with strong and weak chatter, several significant interactions between spectral components are found, suggesting the presence of quadratic type nonlinearities in the dynamics of chatter. By contrast, the dynamics of the chatter-free cutting as the third regime, reflect almost no such interactions. The bicoherence analysis on simultaneously measured time series of three orthogonal components of the main cutting force showed that practically the same information is contained in all three of them
We present a new signal processing and testing technique by using higher statistical moment, the bispectrum, to determine the damping ratio and natural frequency of offshore structures excited by both unexpected Gaussian forces and known non-Gaussian driving forces. Due to the unexpected exciting forces, such as the turbulence, in the ocean environment, the transfer functions of the offshore structures are hardly determined through operating a known driving force and measuring its response. In order to overcome this problem, some of the existing techniques try to model the unexpected forces as white Gaussian forces or almost white Gaussian forces and determine the modal parameters from the response only. Some others are trying to average the input and output in certain effective way to suppress unexpected parts. Our method uses third order moment so as to keep the influence of the unexpected Gaussian forces away from the determination of the transfer function of the structure which has linear properties. We model the third order moment property of the response function with a bispectral model. And the modal parameters can be calculated from the estimated model's coefficients. Our method was proved by a considerable amount of simulations.
LMS algorithms have performance issues related to insufficient
excitation, nonstationary reference inputs, finite-precision arithmetic,
quantization noise, and measurement noise. Such factors cause weight
drift and potential instability in the conventional LMS algorithm. Here,
we analyze the stability and performance of the leaky LMS algorithm,
which is widely used to correct weight drift. A Lyapunov tuning method
is developed to find an adaptive leakage parameter and step size that
provide optimum performance and retain stability in the presence of
measurement noise on the reference input. The method accounts for
nonpersistent excitation conditions and nonstationary reference inputs
and requires no a priori knowledge of the reference input signal other
than a lower bound on its magnitude or a minimum signal-to-noise ratio.
The tuning method is demonstrated for three candidate adaptive leaky LMS
algorithms. Stability and performance tradeoffs of each candidate
Lyapunov tuned algorithm are evaluated experimentally in a single
source, single-point acoustic noise cancellation system
We address the influence of period variation on the Westland
CH-46E helicopter vibration data. The estimation of the time-varying
shaft speed by using a newly developed constrained AR(2) estimator and
the well-known EKF estimator are discussed. The influence that the
period variation captured by these two estimators has on the periodic
time/frequency analysis is illustrated via numerical simulation. This
simulation clearly illustrates a potential spectral smearing if the
period variation is not properly accommodated. A data resampling scheme
is then be proposed to eliminate the spectral smearing effect. The
potential of this scheme is demonstrated via the analysis of the
helicopter vibration data
In this paper, the study of the Wigner–Ville distribution in gearbox condition monitoring is presented. In contrast to other applications of the Wigner–Ville distribution, this paper reports the application of two pattern recognition procedures to detect tooth faults reliably. These procedures are based on statistical and neural pattern recognition. The methods are applied to the detection of a broken tooth in a spur gear.
The ability to predict hazards of mechanical systems accurately can significantly enhance the predictive maintenance task. However, predicting hazards of systems accurately is non-trivial, especially when historical failure data are sparse or zero. The proposed proportional covariate model (PCM) overcomes this difficulty. This paper describes the concepts of PCM briefly and focuses on the estimation of the hazards of mechanical systems using accelerated life tests and condition monitoring data. This new approach to hazard estimation can reduce the number of accelerated life tests significantly. The hazard estimation can further be refined and updated with on-line condition monitoring data on a continual basis.
The need for blindly separating mixtures of signals arises in many signal processing applications. A class of solutions to this problem was recently proposed by the so-called blind source separation (BSS) techniques which rely on the sole knowledge of the number of independent sources present in the mixture. This paper deals with the case where the number of sources is unknown and statistical independence may not apply, but where there is only one signal of interest (SOI) to be separated, which is cyclostationary. It proposes a blind extraction method using a subspace decomposition of the observations via their cyclic statistics. This method is first developed for instantaneous mixtures and is then extended to the convolutive case in the frequency-domain where it does not suffer from the permutation problem as does classical BSS. Experiments on industrial data are finally performed and illustrate the high performance of the proposed method.
This paper presents the application of the spectral kurtosis technique for detection of a tooth crack in the planetary gear of a wind turbine. The work originated from a real case of catastrophic gear failure on a wind turbine, which was not detected by currently applied methods. Nevertheless, several sets of complete vibration data were recorded and analyzed. The authors explored a number of methods commonly applied in online vibration monitoring and diagnostic systems. Those methods did not react to the failure until a few minutes before the failure. Then the method of time domain averaging of the meshing vibration is investigated. In this case, however, averaging does not detect any trace of the tooth crack, primarily because of the extreme frequency range (>four decades) of the fault symptoms. The application of the method is shown, and then the limitations of the averaging in such a case are presented and discussed. Finally, the authors propose a method based on spectral kurtosis, which yields good results. This method was able to detect the existence of the tooth crack several weeks before the gear failure.
A method of detecting transients in mechanical systems by matching wavelets with associated signal is proposed, leading to a development of joint time–frequency–scale distribution. The three variables, the time, frequency and scale, have maximised the chance for finding similar signal segments from a system under inspection. The sensitivity is shown to be very high due to closer matching and better choice of wavelet shapes, which is essential for early fault detection and failure prevention. Fundamental types of wavelets are introduced based on the shapes of widely encountered system responses. A method of processing the three-dimensional image is suggested for interpreting the time–frequency–scale wavelet map, where the properties of the object patterns uncover the features of a signal source, so as to understand the defect and to indicate the condition of a diagnosed system. The joint distribution is demonstrated to be useful in detecting transients from different mechanical systems. Implementation and examples are discussed.
Bearing fault vibrations were modelled as a series of impulse responses of a single-degree-of-freedom. The bearing faults were caused by random fluctuations. The efficient application of self-adaptive noise cancellation (SANC) with conjunction analysis were investigated. Both of the techniques required original signal to be band pass filtered and frequency shifted in order to reduce the samples to be processed by SANC. The two methods reduce the masking in the envelope spectrum. SANC was used to demonstrate the removal of discrete frequency noise. Simulated and vibration signals were used to analyze the envelope spectrum.
This paper develops a unified view of model-based approaches for fault detection and isolation (FDI), taking as a guideline the different levels of the knowledge available about the monitored system. Two functions of the FDI process are distinguished, namely alarm generation and alarm interpretation. The numerical and the qualitative model-based approaches are discussed with respect to these two functions.
Life testing under nominal operating conditions of mechanical parts with high mean lifetime between failure (MTBF) often consumes a significant amount of time and resources, rendering such procedures expensive and impractical. As a result, the technology of accelerated life testing (ALT) has been developed for testing at high stress levels (e.g. temperature, voltage, pressure, corrosive media, load, vibration amplitude, etc.) so that it can be extrapolated—through a physically reasonable statistical model—to obtain estimations of life at lower, normal stress levels or even limit stress levels. However, the issue of prediction accuracy associated with extrapolating data outside the range of testing, or even to a singularity level (no stress), has not yet been fully addressed. In this research, an accelerator factor is introduced into an inverse power law model to estimate the life distribution in terms of time and stresses. Also, a generalized Eyring model is set up for singularity extrapolation in handling limit stress level conditions. The procedure to calibrate the associated shape factors based on the maximum likelihood principle is also formulated. The methodology implementation, based on a one-main-step, multiple-step-stress test scheme, is experimentally illustrated with tapered roller bearing under the stress of environmental corrosion as a case study. The experimental results show that the developed accelerated life test model can effectively evaluate the life probability of a bearing based on accelerated testing data when extrapolating to the stress levels within or outside the range of testing.
Interest in the analysis of random vibrations of mechanical systems started to grow about a half century ago in response to the need for a theory that could accurately predict structural response to jet engine noise and missile launch-induced environments. However, the work that enabled development of the theory of random vibrations started about a half century earlier. This paper discusses contributions to the theory of random vibrations from the time of Einstein to the time of an MIT workshop that was organized by Crandall in 1958.
Continuous-scan laser Doppler vibrometry (CSLDV) is a method whereby one continuously sweeps the laser measurement point over
a structure while measuring, in contrast to the conventional scanning LDV approach where the laser spot remains stationary
while the response is collected at each point. The continuousscan approach can greatly accelerate measurements, allowing one
to capture spatially detailed mode shapes along a scan path in the same amount of time that is typically required to measure
the response at a single point. The method is especially beneficial when testing large structures, such as wind turbines,
whose natural frequencies are very low and hence require very long time records. Several CSLDV methods have been presented
that employ harmonic excitation or impulse excitation, but no prior work has performed CSLDV with an unmeasured, broadband
random input. This work extends CSLDV to that class of input, developing an outputonly CSLDV method (OMA-CSLDV). This is accomplished
by adapting a recently developed algorithm for linear time-periodic systems to the CSLDV measurements, which makes use of
harmonic power spectra and the harmonic transfer function concept developed by Wereley. The proposed method is validated on
a randomly excited free-free beam, where one-dimensional mode shapes are captured by scanning the laser along the length of
the beam. The natural frequencies and mode shapes are extracted from the harmonic power spectrum of the vibrometer signal
and show good agreement with the first seven analytically-derived modes of the beam. The method is then applied to identify
the shapes of several modes of a 20kW wind turbine using a ground based laser and with only a light breeze providing excitation.
This paper addresses the issue of the blind extraction of a second-order cyclostationary source drowned by an unknown number of interferences and additive noise. It first reviews two recently developed methods based respectively on a subspace decomposition of the observed signals via their cyclic statistics and on multiple cyclic regression (MCR). It then proposes a unifying and refined approach using reduced-rank cyclic regression (RRCR) which combines the respective advantages of the two previous methods and suppresses their drawbacks. It also reveals that unlike the classical MCR technique, the power of the additive noise at the output of RRCR does not depend neither on the number of frequency shifts used in the regression nor on the number of available measured signals. This property is verified by means of simulations where the behaviour of all the methods with respect to many parameters is compared. RRCR is finally applied to the diagnostics of bearings and gears where it is shown to achieve a very good extraction of fault signatures.
The strain energy release rate (SERR) theory, combined with Linear Fracture Mechanics and Rotordynamics theories, has been widely used over the last three decades in order to calculate the compliance that causes a transverse surface crack in a rotating shaft. In this paper, the basic theory of this approach is presented, along with some extensions and limitations of its usage. The SERR theory is applied to a rotating crack and gives good results. The linear or nonlinear cracked rotor behavior depends on the mechanism of opening and closure of the crack during the shaft rotation.A brief history of the SERR theory is presented. In the 1970s, this theory met with rotordynamics as a result of research conducted on the causes of rotor failures in power industries. The main goal of this research was to give the engineer an early warning about the cracked situation of the rotor—in other words, to make the identification of the crack possible. Different methods of crack identification are presented here as well as those for multi-crack identification.
The aim of this study is to investigate means of efficiently assessing the effects of distributed structural modification on the dynamic response of a complex structure. Although structural modification has been demonstrated as an efficient method for both 1D structure with distributed modification with/without additional degrees of freedom (DOFs) and 2D structure with distributed modification with reduced DOFs, research into structural modification of 3D structures with additional DOFs has been limited. In this paper, structural modification has been applied to a 3D box frame clamped on one edge or with free–free boundary condition with a plate attached on another side as modification. The frequency response functions (FRFs) of the original unmodified 3D frame were obtained experimentally as well as numerically. The delta dynamic stiffness matrix was determined numerically by modeling the attachment and part of the original structure. The FRFs of the modified 3D frame are computed by coupling the original FRFs and the delta dynamic stiffness matrix. Good agreement is obtained between the FRFs of the modified 3D frame determined experimentally and those obtained by numerical modeling of the complete modified structure. Structural modification method has been verified on 3D structure for distributed modifications with additional DOFs, and also it has been verified on coupling two different types of structures, beam and plate.
In this paper, a wavelet-based demodulating function is proposed to apply in 3D spectral analysis for vibration signals. In the function, there are three parameters required to assign for adjustment and designation of the filtering passband, which are the low cut-off frequency, the high cut-off frequency and the dilation. Accordingly, it would be convenient to apply in the high-frequency resonance technique. In addition, by sweeping the filtering passband from a low-frequency band to a high-frequency band, a 3D spectrum could be constructed to describe how energy distribution between the instantaneous frequency and the filtering passband for a vibration signal. The 3D spectrum would be helpful to give a clear view of both characteristic frequencies and system resonances, and possesses the advantage of minimising the interventions by the end-user.
In the area of modal test/analysis/correlation, significant effort has been expended over the past twenty years in order to make reduced models and to expand test data for correlation and eventual updating of the finite element models. This has been restricted by vibration measurements which are traditionally limited to the location of relatively few applied sensors. Advances in computers and digital imaging technology have allowed 3D digital image correlation (DIC) methods to measure the shape and deformation of a vibrating structure. This technique allows for full-field measurement of structural response, thus providing a wealth of simultaneous test data. This paper presents some preliminary results for the test/analysis/correlation of data measured using the DIC approach along with traditional accelerometers and a scanning laser vibrometer for comparison to a finite element model. The results indicate that all three approaches correlated well with the finite element model and provide validation for the DIC approach for full-field vibration measurement. Some of the advantages and limitations of the technique are presented and discussed.
Two new methods of detecting a fatigue crack in a planet carrier of an epicyclic transmission are developed. These are tested using vibration data from a number of US Army UH-60A Black Hawk helicopter main transmissions. Vibration measurements of faulted and un-faulted transmissions over a range of torque levels in controlled test-cell and on-aircraft conditions are used. The results show that new methods are reliable under test-cell conditions, but less effective under low-torque on-aircraft conditions.
The accuracy of fault diagnostic systems for diesel engine-type generators relies on a comparison of the currently extracted sensory features with those captured during normal operation or the so-called “baseline.” However, the baseline is not easily obtained without the required expertise. Even worse, in an attempt to save costs, many of the diesel engine generators in manufacturing plants are second hand or have been purchased from unknown suppliers, meaning that the baseline is unknown. In this paper, a novel vibration-based fault diagnostic method is developed to identify the vital components of a diesel engine that have abnormal clearance. The advantage of this method is that it does not require the comparison of current operating parameters to those collected as the baseline. First, the nominal baseline is obtained via theoretical modeling rather than being actually captured from the sensory signals in a healthy condition. The abnormal clearance is then determined by inspecting the timing of impacts created by the components that had abnormal clearance during operation. To detect the timing of these impacts from vibration signals accurately, soft-re-sampling and empirical mode decomposition (EMD) techniques are employed. These techniques have integrated with our proposed ranged angle (RA) analysis to form a new ranged angle-empirical mode decomposition method (RA-EMD). To verify the effectiveness of the RA-EMD in detecting the impacts and their times of occurrence, their induced vibrations are collected from a series of generators under normal and faulty engine conditions. The results show that this method is capable of extracting the impacts induced by vibrations and is able to determine their times of occurrence accurately even when the impacts have been overwhelmed by other unrelated vibration signals. With the help of the RA-EMD, clearance-related faults, such as incorrect open and closed valve events, worn piston rings and liners, etc., become detectable even without the comparison to the baseline. Hence, proper remedies can be applied to defective diesel engines to ensure that valuable fuel is not wasted due to the incorrect timing of combustion as well as unexpected fatal breakdown, which may cause loss of production or even human casualties, can be minimized.
In this study, a new mathematical dynamic model of shock absorber is proposed to predict the dynamic characteristics of an automotive system. The performance of shock absorber is directly related to the car behaviours and performance, both for handling and ride comfort. Damping characteristics of automotive can be analysed by considering the performance of displacement-sensitive shock absorber (DSSA) for the ride comfort. The proposed model of the DSSA is considered as two modes of damping force (i.e. soft and hard) according to the position of piston. For the simulation validation of vehicle-dynamic characteristics, the DSSA is mathematically modelled by considering the fluid flow in chamber and valve in accordance with the hard, transient and soft zone. And the vehicle dynamic characteristic of the DSSA is analysed using quarter car model. To show the effectiveness of the proposed damper, the analysed results of damping characteristics were compared with the experimental results, which showed similar behaviour with the corresponding experimental one. The simulation results of frequency response are compared with the ones of passive shock absorber. From the simulation results of the DSSA, it can be concluded that the ride comfort of the DSSA increased at the low-amplitude road condition and the driving safety was increased partially at the high-amplitude road condition. The results reported herein will provide a better understanding of the shock absorber. Moreover, it is believed that those properties of the results can be utilised in the dynamic design of the automotive system.
The use of active non-linear absorber to control the high-amplitude vibration of the non-linear plant subjected to primary external excitation is investigated. The absorber exploits the saturation phenomenon that is known to occur in dynamical systems with quadratic non-linearities and a two-to-one internal resonance. The dynamic behaviour of the plant is described by an oscillator, which includes velocity-dependent damping forces, polynomial and differential-polynomial non-linearities. First, the approximate solutions to the governing equations are obtained by using the method of multiple scales. Then a bifurcation analysis is conducted to examine the stability of the system and the performance of the control strategy is studied. A parametric investigation is carried out to see the effects of changing the damping ratio of the absorber, the value of the feedback gain and the detuning frequency of the absorber on the responses of the plant and absorber. The instantaneous power of the control law is also calculated. Finally, the numerical simulations are performed to demonstrate and validate the saturation control method.
A new kind of shock absorber with Coulomb–fluid damping through coupling oil, wire gauze, rubber and spring by ingenious tactics is designed for reinforcement of electronic-information equipment in atrocious vibration and impact. The physical mechanism of the shock absorber is systematically investigated. The key-model machine shows complex non-linear dynamic characteristics in multi-parameter coupling dynamic test; otherwise, it has a good dynamic performance for attenuating vibration and resisting violent impact. Based on this, the non-linear dynamic model for attenuating vibration mode of the shock absorber is presented by analysing coupling physical mechanism of fluid and Coulomb friction and other factors for designing the shock absorber with high validity. The analytical results obtained in experimental data have been compared with the numerical ones obtained by performing the Runge–Kutta method with the mathematical model. As the model results agree well with the test data, it can be used for engineering design.
Electric vibration absorbers made of distributed piezoelectric devices for the control of beam vibrations are studied. The absorbers are obtained by interconnecting an array of piezoelectric transducers uniformly distributed on a beam with different modular electric networks. Five different topologies are considered and their damping performance is analysed and compared. Their optimal parameters are found by adopting a criterion for critical damping of k̄-waves: the parameters are suitably chosen to have the quickest temporal vibration decay for a single wave number k̄. The analysis is based on homogenized models of the modular piezo-electromechanical systems, i.e. they are regarded as continuous systems by assuming that the number of modules per unit length is high enough with respect to the considered wave numbers. Calling k̄ -absorbers the corresponding optimal absorbers, we show that: (i) k̄-waves are damped in k̄-absorbers with an optimal decay time which is independent of the absorber interconnecting topology, while it depends only on the piezoelectric coupling coefficient; (ii) the efficiency of k̄-absorbers depends significantly on the absorber interconnecting topology for k different from k̄; (iii) one of the proposed absorbers (which is made of a fourth-order electric transmission line with a second-order electric dissipation) equally performs for all the wave numbers and accomplishes an effective multi-modal damping for the mechanically forced response; (iv) the optimal values of the electric parameters differently depend on the number n of used circuit modules for different interconnecting topologies and, in particular, the optimal inductance per module needed in a fourth-order electric transmission line is proportional 1/n3.
Dynamic analysis of a non-linear vehicle model, employing tunable shock absorbers, is presented for random road excitations. A generalised discrete harmonic linearisation technique, based upon a processed energy function, is developed to characterise non-linear restoring and damping forces by an array of equivalent linear stiffness and damping coefficients. An array of locally linear systems is thus formulated to determine the random ride response of the non-linear vehicle model. The simulation results show that the vehicle ride performance can be improved considerably in the frequency range to which the human body is most sensitive, via the tunable shock absorbers.
This paper is focused on the reduction of vibration levels of mechanical systems using dynamic vibration absorbers (DVAs). A general methodology is proposed for the optimum selection of DVA parameters so as to guarantee the efficiency of those devices over a previously selected frequency band. The presented methodology utilises a substructure coupling technique exploring frequency response functions (FRFs), which enables one to calculate the FRFs of the composite structure (primary system+DVAs), from the FRFs of the primary structure and the theoretical expressions of the FRFs of the DVAs. The FRFs of the composite structure, which are expressed as functions of the DVA parameters, are then used to define scalar performance indexes related to the vibration levels of the composite structure over the selected frequency band. These performance indexes are optimised with respect to the DVA parameters by solving a general non-linear constrained optimisation problem. The first part of the paper is devoted to the formulation of the substructure coupling method and the optimisation procedures. Numerical applications using experimentally acquired FRFs are then presented to illustrate the main features of the proposed methodology.
The abiding problem of vibration absorption has occupied engineering scientists for over a century and there remain abundant examples of the need for vibration suppression in many industries. For example, in the automotive industry the resolution of noise, vibration and harshness (NVH) problems is of extreme importance to customer satisfaction. In rotorcraft it is vital to avoid resonance close to the blade passing speed and its harmonics. An objective of the greatest importance, and extremely difficult to achieve, is the isolation of the pilot's seat in a helicopter. It is presently impossible to achieve the objectives of vibration absorption in these industries at the design stage because of limitations inherent in finite element models. Therefore, it is necessary to develop techniques whereby the dynamic of the system (possibly a car or a helicopter) can be adjusted after it has been built. There are two main approaches: structural modification by passive elements and active control. The state of art of the mathematical theory of vibration absorption is presented and illustrated for the benefit of the reader with numerous simple examples.
Many damage detection and system identification approaches benefit from the availability of both acceleration and displacement measurements. This is particularly true in the case of suspected non-linear behavior and permanent deformations. In civil and mechanical structural modeling accelerometers are most often used, however displacement sensors, such as non-contact optical techniques as well as GPS-based methods for civil structures are becoming more common. It is suggested, where possible, to exploit the inherent redundancy in the sensor information and combine the collocated acceleration and displacement measurements in a manner which yields highly accurate motion data. This circumvents problematic integration of accelerometer data that causes low-frequency noise amplification, and potentially more problematic differentiation of displacement measurements which amplify high-frequency noise. Another common feature of displacement-based sensing is that the high-frequency resolution is limited, and often relatively low sampling rates are used. In contrast, accelerometers are often more accurate for higher frequencies and higher sampling rates are often available. The fusion of these two data types must, therefore, combine data sampled at different frequencies. A multi-rate Kalman filtering approach is proposed to solve this problem. In addition, a smoothing step is introduced to obtain improved accuracy in the displacement estimate when it is sampled at lower rates than the corresponding acceleration measurement. Through trials with simulated data the procedure's effectiveness is shown to be quite robust at a variety of noise levels and relative sample rates for this practical problem.
The fatigue-related behavior of a linear elastic system (LES) can be efficiently identified using acceleration response if the frequency response function between the acceleration input and the stress response (FRFas) can be predetermined. In this paper, the spectral damage of an LES is predicted using energy isoclines, whose function consists of both FRFas and the fatigue material properties of the LES. The accuracy of the proposed method was verified through a uniaxial vibration test using flexible specimens and a comparison of the acceleration-based and strain-based spectral damage at the location of interest.
The work described here concerns the bandwidth enhancement of any low bandwidth position measurement device by using acceleration measurements to provide high frequency motion information. The emphasis is on the mechanism for combining the two types of measurements effectively, rather than the measurement transducers themselves. Alternative procedures for combining position and acceleration information are examined, along with relevant considerations. Digital implementation of the signal processing is chosen and the effects of sampling rates, quantisation and roundoff on overall accuracy assessed quantitatively. The conclusions from the analysis are used to help determine the signal processing details. In addition, implications of using the measurement scheme in closed loop position control applications are explicitly considered. The feasibility of the computational scheme has been established by experimental tests under open loop and closed loop position control conditions. A 16-bit microprocessor/coprocessor combination was used and was successful in increasing the bandwidth of accurate position measurement from 16 Hz to well over 40 Hz. Specific recommendations to improve overall computational accuracy are given and are easily realisable using more powerful microcomputing equipment than the one used here.
An adaptive mode superposition and acceleration technique (AMSAT) is proposed and implemented into the computation of frequency response functions (FRFs) and their sensitivities. Based on the mode superposition and mode acceleration methods for the FRFs, m-version, s-version, and ms-version adaptive schemes are presented. In these schemes, the error resulted from the mode truncation and/or series truncation is, at first, estimated at every specific frequency, respectively. Then, one more mode (called m-version), or one more level of the series (called s-version), or the combination (called ms-version) is included in the computation of the FRF when its error is greater than the error tolerance. The new FRF is recalculated and its error is re-evaluated. This procedure is repeated until all the errors fall below the specified value. Although only the implementation of FRFs and their sensitivities is demonstrated in this paper, the proposed adaptive technique may be applied to the computation of dynamic responses in time domain and their sensitivities, sensitivity of eigenpairs, modal energy, etc. One numerical example is included to demonstrate the application of the proposed adaptive schemes. The results show that the present schemes work very well. The s- and ms-version adaptive schemes are much more efficient than m-version scheme. Since the intention of this paper is to propose these new procedures, the damping, particularly the non-classical damping, is not included due to the complexity.
The zero-crossing averaging method (ZAM), which was originally developed for improving the measurement accuracy of force by means of the levitation mass method (LMM), is applied for evaluating the impact response of accelerometers. In the ZAM, the moment of the zero-crossing point is calculated as the average of many adjacent zero-crossing points and then the frequency is calculated. In this paper, the impulse response of an accelerometer is evaluated with high resolution and high sampling rate by means of the ZAM. The present status and future prospects of the ZAM as a method for use in calibration of accelerometers are discussed.
This paper presents a comparative study between accelerometer and laser vibrometer measurements aimed at on-line quality control carried out on the universal motors used in washing machines, which exhibit defects localised mainly in the bearings, including faults in the cage, in the rolling element and in the outer and inner ring. A set of no defective and defective motors were analysed by means of the acceleration signal provided by the accelerometer, and the displacement and velocity signals given by a single-point laser vibrometer. Advantages and disadvantages of both absolute and relative sensors and of contact and non-contact instrumentation are discussed taking into account the applicability to real on-line quality control measurements and bringing to light the related measurement problems due to the specific environmental conditions of assembly lines and sensor installation constraints. The performance of different signal-processing algorithms is discussed: RMS computation at steady-state proves effective for pass or fail diagnosis, while the amplitude of selected frequencies in the averaged spectra allows also for classification of a variety of special faults in bearings. Joint time–frequency analysis output data can be successfully used for pass or fail diagnosis during transients, thus achieving a remarkable reduction in testing time, which is important for on-line diagnostics.
Proper pretest planning is a vital component of any successful vibration test. An extremely important part of the pretest exercise is the placement of sensors, usually in the form of accelerometers. The accelerometers must be placed such that all of the important dynamic information is obtained during the course of the test. The resulting sensor configuration must be optimal in some sense such that test resources are conserved. The state-of-the-practice is to select individual sensor location/directions from a candidate set based upon one of several available criteria. Triaxial accelerometers are then placed at the corresponding locations. In general, this results in the non-optimal placement of many of the accelerometers. This paper presents a new technique, based upon Effective Independence, that places triaxial accelerometers as single units in an optimal fashion. The technique is applied and compared with standard approaches using the X-33 vehicle.
Model-based diagnostic techniques can be used successfully in the health analysis of rotormachinery. Unfortunately, a poor accuracy of the model of the fully assembled machine, as well as errors in the evaluation of the experimental vibrations caused only by the impending fault, can affect the accuracy of fault identifications. This can make difficult to identify the type of the actual fault as well as to evaluate its severity and its position. This paper shows some methods that have been developed to measure the accuracy of the results obtained with model-based techniques aimed to identify faults in rotating machines. The testing of the capabilities of these methods is carried out using both machine response simulated with mathematical models and experimental data on a real machine.
This paper presents a comparative study of three high-accuracy frequency estimation methods for application in vibration analysis of rotating machinery. The first two techniques are non-parametric methods based on the fast Fourier transform (FFT) : the interpolated fast Fourier transform (IFFT) and the iterative weighted phase averager (IWPA). The third method is a parametric high-resolution technique known as ESPRIT. The FFT-based methods combine techniques to reduce the effects of windowing with an iterative procedure which, at each iteration, detects the strongest peak and subtracts its effect (to reduce the interference resulting from spectral leakage). The paper compares their variance, resolution and computational requirements by means of simulation examples and also using end winding vibration data taken from a hydroelectric turbogenerator. It is found that, in situations with a moderate or high level of spectral interference, the IWPA method outperforms the IFFT and is even competitive with ESPRIT. Moreover, the IWPA has the ability to separate sinusoids more closely spaced than the periodogram's resolution limit. The IFFT method, on the other hand, has the lowest computational cost.
This is the first of two companion papers which summarise the theoretical and experimental work aimed at developing a generalised, acoustic-based sensing strategy for free and semi free field problems. The aim of the work is the design of practical acoustic sensing systems for active noise control of large complex noise sources, based on data fusion of a large number of sensor signals. A wide breath of literature illustrates several practical advantages to pursuing a sensing system which measures orthogonal functions with respect to a global error, and how a large number of point sensors are required in the filtering process. For this reason we examine modal filtering of orthogonal functions for two-dimensional noise sources and highlight the practicalities of sensing systems which measure the associated constituents. We compare three variations of orthogonally radiating shapes based on structural modes, structural elements and combinations of in-/out-of-phase acoustic monopoles. Comparisons are made based on the number of constituents required to estimate 90% of radiated power; the modal filtering weights frequency dependence; and simulated decompositions of a sound pressure field to radiated power. Of the sensing strategies which are structural specific, we extend them to facilitate the use of acoustic sensors to measure the orthogonal “structural” patterns.
For many of the large radiating structures targeted for active noise control, the number of sensors required in the system to achieve global sound control is beyond what can be practically handled as inputs to the control algorithm. In an attempt to overcome this problem, many researchers have turned their attention to a number of variants of modal filtering. However, developments to date have required some a priori knowledge of structural vibration characteristics, such as mode shapes. This limits application to simple structures. What is presented here is an alternative approach to the modal filtering exercise, where the radiated sound field is decomposed using fundamental acoustic quantities. This makes it possible to design an optimised sensing system, one which facilitates the greatest levels of disturbance attenuation for the minimum number of inputs, without detailed knowledge of the vibration characteristics of the target structure.
This paper presents a finite element modelling of flexural actuation of an aluminium cantilever beam by two thin plates made of piezoelectric PZT-ceramic material. An analytical study describes the actuators as flexural wave-source into the beam that once excited radiates sound waves into the surrounding air. FEM-calculations of piezoelectric–mechanical–acoustic aspects correlated together are then conducted with ANSYS that has been chosen for its coupled-field modelling capabilities. As the PZT-plates are polarised in their thickness direction but operate in the plane dimension, their input material properties are orthotropic and characterised by the three, stiffness, dielectric and piezoelectric, matrices. The finite element analysis takes into account a physical adhesive bonding between actuators and beam, as well as beam damping conditions. Sound radiation of the vibrating beam is calculated within an air sphere surrounding the beam and in contact with it by a fluid–structure interaction zone. Results are given in the form of spatial distributions of sound pressure and frequency response functions. A complete calculation example is also given for the sixth flexural vibration eigenmode at 1550 Hz of the beam. Validation of the numerical results is conducted through measurements for both piezoelectric–mechanical and mechanical–acoustic couplings.
Vibration analysis is widely used in machinery diagnostics and the wavelet transform has also been implemented in many applications in the condition monitoring of machinery. In contrast to previous applications, this paper examines whether acoustic signal can be used effectively along vibration signal to detect the various local faults in gearboxes using the wavelet transform. Two commonly encountered local faults, tooth breakage and tooth crack, were simulated. The results from acoustic signals were compared with vibration signals. The results suggest that acoustic signals are very affective for the early detection of faults and may provide a powerful tool to indicate the various types of progressing faults in gearboxes.
Detecting and locating damage in structural components and joints that have high feature densities and complex geometry is a difficult problem in the field of structural health monitoring (SHM). Active propagation of diagnostic waves is one approach that is used to detect damage. But small cracks and damage are difficult to detect because they have a small effect on the propagating waves as compared to the effects the complex geometry itself which causes dispersion and reflection of waves. Another limitation of active wave propagation is that pre-damage data is required for every sensor–actuator combination, and a large number of sensors might be needed to detect small cracks on large structures. Overall, the problem of detecting damage in complex geometries is not well investigated in the field of SHM. Nevertheless, the problem is important because damage often initiates at joints and locations where section properties change.
This paper presents a strategy for the application of acoustic beamforming to locate noise sources in a reverberant field.In the hypothesis of stationary phenomena, the average amplitude and standard deviation of the output of beamforming, obtained from different array locations, are calculated.The standard deviation, normalized by the maximum value, can be used for beamforming output weighting, so as to enhance the source contribution, which is space invariant, and to attenuate the mirrors and sidelobe peaks, whose spatial position changes with changes in array position.The availability of microphone signals acquired when moving the array to a different position also allows a super-array to be obtained, i.e. an array obtained considering all the data as coming from a unique array. In this way, the capability of the averaging procedure to reject mirrors effects and disturbances is combined with high resolution beamforming for application in reverberant fields. These improvements are extended to the entire frequency range, since the procedure is not greatly affected by signal wavelength.
A coupled structural–electrical finite element model for the active control of the non-linear vibration of a composite panel bonded with piezoelectric materials under random excitation is presented in this paper. The von Karman non-linear strain–displacement relations for large deflection responses and linear piezoelectricity constitutive relations are employed. A new non-linear modal finite element formulation is developed for symmetrical vibration that differs from the models in previous studies in that the first-order non-linear terms, which depend on the unknown transverse displacement, are eliminated. The system equations of motion are transformed into a set of non-linear equations in modal coordinates. The advantage of this non-linear modal transformation method is that the sizes of the non-linear matrices are reduced drastically. The transformed system equations are then written in the state space format. Four different control methods—velocity feedback, lead, lag, and H∞—are employed and examined for cases of small- and large-amplitude vibrations. The effects of truncated modes on the control performance and comparisons of the control methods are studied.
The monitoring of progressive wear in gears using various non-destructive technologies as well as the use of advanced signal processing techniques upon the acquired recordings to the direction of more effective diagnostic schemes, is the scope of the present work. For this reason multi-hour tests were performed in healthy gears in a single-stage lab scale gearbox until they were seriously damaged. Three on-line monitoring techniques are implemented in the tests. Vibration and acoustic emission recordings in combination with data coming from oil debris monitoring (ODM) of the lubricating oil are utilized in order to assess the condition of the gears. A plethora of parameters/features were extracted from the acquired waveforms via conventional (in time and frequency domain) and non-conventional (wavelet-based) signal processing techniques. Data fusion was accomplished in the level of integration of the most representative among the extracted features from all three measurement technologies in a single data matrix. Principal component analysis (PCA) was utilized to reduce the dimensionality of the data matrix whereas independent component analysis (ICA) was further applied to identify the independent components among the data and correlate them to different damage modes of the gearbox. Finally heuristic rules based on characteristic values of the resulted independent components were set, realizing thus a health monitoring scheme for gearboxes.The integration of vibration, AE and ODM data increases the diagnostic capacity and reliability of the condition monitoring scheme concluding to very interesting results. The present work summarizes the joint efforts of two research groups towards a more reliable condition monitoring of rotating machinery and gearboxes specifically.
An acoustic non-invasive method for the diagnosis of detachment in frescos was previously proposed by the authors. This method is based on the indirect evaluation of the vibrations due to detachments, by means of a surface inspection. In this paper the relations between the dynamics of the structure to be inspected and the operational principles of the acoustic method of diagnosis are presented. The dynamic analysis is carried out using experimental investigations and analytical and numerical models. It shows that the quality of the diagnosis depends on the capability of the acoustic device to excite the structural resonances related to the detachments. These results are useful for future improvements, in particular to enhance the sensitivity of the proposed method.
Vibration monitoring of rolling element bearings is probably the most established diagnostic technique for rotating machinery. The application of acoustic emission (AE) for bearing diagnosis is gaining ground as a complementary diagnostic tool, however, limitations in the successful application of the AE technique have been partly due to the difficulty in processing, interpreting and classifying the acquired data. Furthermore, the extent of bearing damage has eluded the diagnostician. The experimental investigation reported in this paper was centred on the application of the AE technique for identifying the presence and size of a defect on a radially loaded bearing. An experimental test rig was designed such that defects of varying sizes could be seeded onto the outer race of a test bearing. Comparisons between AE and vibration analysis over a range of speed and load conditions are presented. In addition, the primary source of AE activity from seeded defects is investigated. It is concluded that AE offers earlier fault detection and improved identification capabilities than vibration analysis. Furthermore, the AE technique also provided an indication of the defect size, allowing the user to monitor the rate of degradation on the bearing; unachievable with vibration analysis.
Acoustic methods are among the most useful techniques for monitoring the condition of machines. However, the influence of background noise is a major issue in implementing this method. This paper introduces an effective monitoring approach to diesel engine combustion based on acoustic one-port source theory and exhaust acoustic measurements. It has been found that the strength, in terms of pressure, of the engine acoustic source is able to provide a more accurate representation of the engine combustion because it is obtained by minimising the reflection effects in the exhaust system. A multi-load acoustic method was then developed to determine the pressure signal when a four-cylinder diesel engine was tested with faults in the fuel injector and exhaust valve. From the experimental results, it is shown that a two-load acoustic method is sufficient to permit the detection and diagnosis of abnormalities in the pressure signal, caused by the faults. This then provides a novel and yet reliable method to achieve condition monitoring of diesel engines even if they operate in high noise environments such as standby power stations and vessel chambers.
Vibration analysis is widely used in machinery diagnostics and the Wigner–Ville distribution has also been implemented in many applications in the condition monitoring of machinery. In contrast to previous applications, this paper examines whether acoustic signal can be used effectively to detect the various local faults in gearboxes using the smoothed pseudo-Wigner–Ville distribution. Three types of progressing local faults, broken tooth, gear crack and localised wear, were simulated. The results from acoustic signals were compared with vibration signals. The results suggest that acoustic signals are very affective for the early detection of faults and may provide a powerful tool to indicate the various types of progressing faults in gearboxes.