Self-affine and ARX-models zonation of well logging data

Zonation of time series into models which their parameters are piecewise constant are important and well-studied problems. Geophysical well logging data often show a complex pattern due to their multifractal nature. In a multifractal system, any pieces of it are established by a distinct exponent that can characterize them. This feature has the capability to cluster them. Self-affine zonation by Auto Regressive model with exogenous inputs (ARX) is a new approach which places well logging segments in the clusters which are more self-affine against the other clusters. This approach was performed and compared with a conventional ARX zonation in the well logging data of three different oilfields in southern parts of Iran. The results showed a good accuracy for detecting homogeneous lithological segments and led to a precise interpretation process to update the reservoir architecture.     

Identification of hybrid ARX-neural network models for three-dimensional simulation of a vibroacoustic system

Acoustic noise in industrial areas, typically generated by compressors and vacuum pumps, may be mitigated by the combined use of passive and active noise control strategies. Despite its widespread use, the traditional Active Noise Control (ANC) technique requires error feedback and has been proven to be effective only within a small spatial region. When the movement of human ears is required within a large region and error feedback is difficult to be accomplished, new cancelling strategies have to be devised to achieve acceptable levels of spatial coverage. In the pursuit of this goal, this paper proposes a vibroacustic model to predict noise radiated from machinery. The model output is the sound signal of the noise at a given point inside a closed room. The two model inputs are the vibration signal at the noise source and the spatial coordinates of the intended point. Experimental output data were measured at several points inside a region defined by a solid rectangle. A fixed-order ARX model was chosen (AutoRegressive with eXogenous input), and for each spatial point and its corresponding pair of input-output signals, a set of parameter values was estimated. To integrate all these models into a single one, a neural network was employed to associate or approximate each set of parameters to its spatial coordinates. With this approach, the total number of parameters is expected to be greatly reduced, when considering the original separated models. Experimental results are presented and comparisons with other models are established on the basis of least-square error metrics and parsimony of parameters. A qualitative perspective for employing the proposed model in the design of large-region ANC strategies is also offered.     

Intelligent Online Monitoring of Rolling Bearing: Diagnosis and Prognosis

This paper suggests a new method to predict the Remaining Useful Life (RUL) of rolling bearings based on Long Short Term Memory (LSTM), in order to obtain the degradation condition of the rolling bearings and realize the predictive maintenance. The approach is divided into three parts: the first part is the clustering to detect the damage state by the density-based spatial clustering of applications with noise. The second one is the health indicator construction which could give a better reflection of the bearing degradation tendency and is selected as the input for the prediction model. In the third part of the RUL prediction, the LSTM approach is employed to improve the accuracy of the prediction. The rationale of this work is to combine the two methods—the density-based spatial clustering of applications with noise and LSTM—to identify the abnormal state in rolling bearings, then estimate the RUL. The suggested method is confirmed by experimental data of bearing life cycle, and the RUL prediction results of the model LSTM are compared with the nonlinear au-regressive model with exogenous input model. In addition, the constructed health indicator is compared with the spectral kurtosis feature. The results demonstrated that the suggested method is more appropriate than the nonlinear au-regressive model with exogenous input model for the prediction of bearing RUL.     

STRUCTURAL DAMAGE DETECTION BASED ON A MICRO-GENETIC ALGORITHM USING INCOMPLETE AND NOISY MODAL TEST DATA

This paper describes a procedure for detecting structural damage based on a micro-genetic algorithm using incomplete and noisy modal test data. As the number of sensors used to measure modal data is normally small when compared with the degrees of freedom of the finite element model of the structure, the incomplete mode shape data are first expanded to match with all degrees of freedom of the finite element model under consideration. The elemental energy quotient difference is then employed to locate the damage domain approximately. Finally, a micro-genetic algorithm is used to quantify the damage extent by minimizing the errors between the measured data and numerical results. The process may be either of single-level or implemented through two-level search strategies. The study has covered the use of frequencies only and the combined use of both frequencies and mode shapes. The proposed method is applied to a single-span simply supported beam and a three-span continuous beam with multiple damage locations. In the study, the modal test data are simulated numerically using the finite element method. The measurement errors of modal data are simulated by superimposing random noise with appropriate magnitudes. The effectiveness of using frequencies and both frequencies and mode shapes as the data for quantification of damage extent are examined. The effects of incomplete and noisy modal test data on the accuracy of damage detection are also discussed.     

FRF-based damage localization method with noise suppression approach

In this paper a noise-robust damage identification method is presented for localization of structural damage in presence of heavy noise influences. The method works based on Frequency Response Functions (FRFs) of the damaged structure without any prior knowledge of the healthy state. The main innovation of this study starts with convolving FRFs with Gaussian kernel to suppress the noise. Denoised signals are then used to develop shape signals according to the second derivative of the operational mode shapes at frequencies in the half-power bandwidth of the center resonant frequencies. The scheme is followed by normalization of shape signals to create a two-dimensional map indicating the damage pattern. The validation of the method was carried out based on simulated data and experimental measurements. The simulated data polluted with 10 percent random noise considering four different conditions: (i) un-correlated noise with Gaussian distribution (ii) noise with non-Gaussian exponential distribution (iii) noise with non-Gaussian Log-normal distribution and (iv) correlated colored noise. The robustness of the method was examined with respect to the damage severity with various damage conditions. Finally, damage detection experiments of a fixed–fixed steel beam are presented to illustrate the feasibility and effectiveness of the proposed method. According to the numerical and experimental investigations, it was demonstrated that the proposed approach presents satisfactory damage indices both in single and multiple damage states in presence of high level noise. Hence, the method can overcome the problems of output measurement noise and deliver encouraging results on damage localization.     

Structural damage detection of controlled building structures using frequency response functions

If a building structure requires both a vibration control system and a health monitoring system, the integration of the two systems will be cost-effective and beneficial. One of the key problems of this integrated system is how to use control devices to enhance system identification and damage detection. This paper presents a new method for system identification and damage detection of controlled building structures equipped with semi-active friction dampers through model updating based on frequency response functions. The two states of the building are first created by adding a known stiffness using semi-active friction dampers. A scheme based on the frequency response functions of the two states of the building is then presented to identify stiffness parameters of structural members in consideration of structural connectivity and transformation information. By applying the proposed model updating scheme to the damaged building, a damage detection scheme is proposed based on the identified stiffness parameters of structural members of both the original and damaged buildings. The feasibility of the proposed schemes is finally demonstrated through a detailed numerical investigation in terms of an example building, in which the effects of measurement noise and excitation conditions are discussed. The numerical results clearly show that the proposed method can locate and quantify damage satisfactorily even though measurement noise is taken into consideration.     

A sensitivity-based structural damage identification method with unknown input excitation using transmissibility concept

Unknown input excitation and local damages universally coexist in a practical situation. Therefore, in this paper a structural damage identification method based on the transmissibility concept in state space domain is proposed without the need for input measurements. On the basis of the transformation matrix which is computed using the system Markov parameters in state space, the relationship between two different sets of acceleration response measurements can be formulated under the same input excitation. A sensitivity-based model updating approach is applied to identify the local damages by minimizing the difference between the measured response and the reconstructed response. The sensitivity of the dynamic acceleration response with respect to the elemental stiffness factors is derived analytically in the state space domain, which accelerates the process of damage identification. A numerical cantilever beam is employed to validate that the variation of structural parameters induced by the local damages can be accurately and effectively identified without the input excitation information by the proposed method even with measurement noise considered. A laboratory test is further carried out to verify the proposed structural damage identification method based on the response reconstruction technique.     

Damage identification in beam type structures based on statistical moment using a two step method

This paper defines a novel damage index-strain statistical moment, and formulates the fourth strain statistical moment (FSSM) of beam-type structures under white noise excitation. Based on this newly defined strain statistical moment index and the least square optimization algorithm, a two-step damage identification method is proposed. This two-step method is operated like this: first use the difference curves of FSSMs before and after damage to locate damage elements; then for those identified damage elements, employ the model updating method based on the least square algorithm to assess their damage severity. Numerical studies on a simply supported beam and a two-span continuous beam are performed and the study results show that the newly defined index is effective to locate damages, even when the noise intensity is as high as 15 percent. Integrating with the least square-based model updating technique, the damage severities of beam-type structures can also be determined quantitatively. In this way, the proposed two-step method is verified and found to be capable of identifying damage positions and severities of beam-type structures and insensitive to measurement noise.     

Damage in fiber bundle models

We introduce a continuous damage fiber bundle model and compare its behavior with that of dry fiber bundles. Several interesting constitutive behaviors, such as plasticity, are found in this model depending on the value of the damage parameter and on the form of the disorder distribution. We compare the constitutive behavior of global load transfer models, obtained analytically, with local load transfer models numerical simulations. The evolution of the damage is studied analyzing the cluster statistics for dry and continous damage fiber bundles. Finally, it is shown that quenched random thresholds enhance damage localization. Received 27 March 2000     

Interpolation of aerodynamic damping of lifting rotors in forward flight from measured response variance

With the necessity of experimentally measuring the aerodynamic derivatives of lifting rotors in forward flight, it becomes desirable for reasons of parametric resonance to measure the variance data of the response to white noise inputs, and then to interpolate with the numerically computed variance values for different assumed values of the damping parameter or the inertia number. Accordingly, methods are developed to compute directly the blade response variance matrix up to high rotor advance ratios for a series of inertia numbers. Numerical results refer to a rigid blade flapping model with an elastically restrained flapping hinge at the rotor centre. Different combinations of the advance ratio, tip-loss factor, flapping restraint parameter and inertia number are included. The white noise excitation is treated without and with input modulation, the latter case including azimuthwise blade input variation. The mean square response study of the model shows that up to an advance ratio of the order of 0·3 and at conventional values of the inertia number the perturbation approach is satisfactory. The numerical scheme, in addition to solving directly the response variance equations which are similar in structure to the original blade dynamic equations, makes use of the fact that the variable part of system parameter functions are independent of the inertia number. Compared to earlier studies the methods therefore offer significant saving in machine time. Numerical results pertaining to previously proposed experimental and analytical models show excellent agreement.     

An expert system for predicting nonlinear aeroelastic behavior of an airfoil

In this paper we present an expert system to perform steady-state response predictions. We consider an aeroelastic model simulating a two degree-of-freedom airfoil oscillating in pitch and plunge with a freeplay nonlinearity in the pitch degree-of-freedom. In the proposed data-driven methodology, a freeplay is first confirmed, and then the locations of the switching points are determined. A state-space formulation is constructed to model the piece-wise linear system. The parameters of the system are estimated using the Kalman filter and the expectation maximization algorithm. The attractive feature of the present approach is its ability to accurately predict the steady-state behavior of the nonlinear aeroelastic system with freeplay, using only a limited amount of transient input data. To demonstrate the effectiveness of the proposed methodology, we present applications to freeplay aeroelastic data arising from wind tunnel experiments and numerical simulations.     

The design of synthesized structural acoustic sensors for active control of interior noise with experimental validation

In this paper, the feasibility of using synthesized structural acoustic sensors (SSAS) for active noise control inside irregularly shaped enclosures is investigated. A SSAS consists of a cluster of inter-connected discrete PVDF elements, located on the surface of a vibrating structure enclosing a sound field. An optimal design ensures the sensor output to be directly related to the acoustical potential energy inside the enclosure. Hence, synthesized structural acoustic sensors can provide error signals for an active noise control system, and the use of microphones inside the enclosure can be avoided. A cylindrical shell with a floor partition, which can be used to model an aircraft cabin, is used as a test case. PZT actuators are used as control actuators. Both SISO (single input and single output) and MIMO (multi-input and multi-output) control systems are optimally designed using Genetic Algorithms and implemented with a Filtered-X Feedforward LMS (least-mean-square) controller. Their control performances are evaluated with different types of disturbances. To show the effectiveness of the optimal design approach, some non-optimal control systems are also tested and compared with the optimal one. It is shown that with optimally designed SSAS, an active structural acoustic control system can effectively reduce noise inside the enclosures without using any acoustic transducers.     

EXTRACTION OF STRUCTURAL SYSTEM MATRICES FROM AN IDENTIFIED STATE-SPACE SYSTEM USING THE COMBINED MEASUREMENTS OF DVA

A time domain method for the extraction of the structural system matrices (mass, damping and stiffness matrices) from an identified state-space system is proposed in this paper using the combined measurements of displacement, velocity and acceleration (DVA) together with the input excitations. The method is based on the invariance of continuous-time Markov parameters. An explicit expression of the relationship between the continuous-time Markov parameters, the structural system matrices, and the influence matrices for output DVA as well as the input force has been derived. The determination of structural system matrices is also valid when only the displacement, velocity or acceleration responses are measured. In this paper, the equivalent state system matrices are obtained by an algorithm, which combines the eigensystem realization algorithm (ERA) and the autoregressive with exogeneous (ARX) model. The ARX model provides the necessary discrete-time Markov parameters from the measured input and output data, and then the equivalent state system matrices are identified from discrete-time Markov parameters by using the ERA. A lumped mass model with three degrees of freedom is employed to illustrate the accuracy and feasibility of the presented method.     

An adhesive bond state classification method for a composite skin-to-spar joint using chaotic insonification

The combination of chaotically amplitude-modulated ultrasonic waves and time series prediction algorithms has shown the ability to locate and classify various bond state damage conditions of a composite bonded joint. This study examines the ability of a new two-part supervised learning classification scheme not only to classify disbond size but also to classify whether a bond for which there is no baseline data is undamaged or has some form of disbond. This classification is performed using data from a similarly configured composite bond for which baseline data are available. The test structures are analogous to a wing skin-to-spar bonded joint. An active excitation signal is imparted to the structure through a macro fiber composite (MFC) patch on one side of the bonded joint and sensed using an equivalent MFC patch on the opposite side of the joint. There is an MFC actuator/sensor pair for each bond condition to be identified. The classification approach compares features derived from an autoregressive (AR) model coefficient vector cross-assurance criterion.     

Nonlinear finite element model updating of an infilled frame based on identified time-varying modal parameters during an earthquake

A model updating methodology is proposed for calibration of nonlinear finite element (FE) models simulating the behavior of real-world complex civil structures subjected to seismic excitations. In the proposed methodology, parameters of hysteretic material models assigned to elements (or substructures) of a nonlinear FE model are updated by minimizing an objective function. The objective function used in this study is the misfit between the experimentally identified time-varying modal parameters of the structure and those of the FE model at selected time instances along the response time history. The time-varying modal parameters are estimated using the deterministic–stochastic subspace identification method which is an input–output system identification approach. The performance of the proposed updating method is evaluated through numerical and experimental applications on a large-scale three-story reinforced concrete frame with masonry infills. The test structure was subjected to seismic base excitations of increasing amplitude at a large outdoor shake-table. A nonlinear FE model of the test structure has been calibrated to match the time-varying modal parameters of the test structure identified from measured data during a seismic base excitation. The accuracy of the proposed nonlinear FE model updating procedure is quantified in numerical and experimental applications using different error metrics. The calibrated models predict the exact simulated response very accurately in the numerical application, while the updated models match the measured response reasonably well in the experimental application.     

Pseudo field modulation in EPR spectroscopy

This paper develops methodology for computer simulation of the effect on an experimental EPR spectrum that would occur if an additional field modulation were applied followed by eventual phase sensitive detection at the modulation frequency or at one its harmonics. The algorithm, which is called pseudomodulation, transforms the digitized spectrum and also filters the noise. If a second harmonic spectrum is desired in order to make subtle changes in curvature more apparent, it is shown that it is always preferable to obtain an experimental second harmonic spectrum. The signals are identical, but because of the filtering properties of the pseudomodulation algorithm, the noise is lower. Pseudomodulation should be applied to simulated spectra prior to fitting a model to data in order more precisely to simulate the experimental signal. It is argued that such fits ought to involve not only first harmonics but also higher harmonics, since the various harmonics are sensitive in different ways to input parameters in the spin Hamiltonian. Application of pseudomodulation to the EPR spectrum of the blue copper-protein azurin is described.     

Mode shape expansion using perturbed force approach

A new approach for expanding incomplete experimental mode shapes is presented which considers the modelling errors in the analytical model and the uncertainties in the vibration modal data measurements. The proposed approach adopts the perturbed force vector that includes the effect of the discrepancy in mass and stiffness between the finite element model and the actual tested dynamic system. From the developed formulations, the perturbed force vector can be obtained from measured modal data and is then used for predicting the unmeasured components of the expanded experimental mode shapes. A special case that does not require the experimental natural frequency in the mode shape expansion process is also discussed. A regularization algorithm based on the Tikhonov solution incorporating the generalized cross-validation method is employed to filter out the influence of noise in measured modal data on the predictions of unmeasured mode components. The accuracy and robustness of the proposed approach is verified with respect to the size of measured data set, sensor location, model deficiency and measurement uncertainty. The results from two numerical examples, a plane frame structure and a thin plate structure, show that the proposed approach has the best performance compared with the commonly used existing expansion methods, and can reliably produce the predictions of mode shape expansion, even in the cases with limited modal data measurements, large modelling errors and severe measurement noise.     

Statistical damage identification of structures with frequency changes

Model updating methods based on structural vibration data have being rapidly developed and applied to detect structural damage in civil engineering. But uncertainties existing in the structural model and measured vibration data might lead to unreliable damage detection. In this paper a statistical damage identification algorithm based on frequency changes is developed to account for the effects of random noise in both the vibration data and finite element model. The structural stiffness parameters in the intact state and damaged state are, respectively, derived with a two-stage model updating process. The statistics of the parameters are estimated by the perturbation method and verified by Monte Carlo technique. The probability of damage existence is then estimated based on the probability density functions of the parameters in the two states. A higher probability statistically implies a more likelihood of damage occurrence. The presented technique is applied to detect damages in a numerical cantilever beam and a laboratory tested steel cantilever plate. The effects of using different number of modal frequencies, noise level and damage level on damage identification results are also discussed.     

A numerically-enhanced machine learning approach to damage diagnosis using a Lamb wave sensing network

This paper describes a methodology for the design of a model-based diagnostic unit. The objective of the work is to define a suitable procedure for the design and verification of diagnostic performance in a simulated environment, trying to maximise the generalisation capability of pattern recognition algorithms when tested with real experimental signals. The system is designed and experimentally verified to solve the fatigue crack damage localisation and assessment problems in a realistic, though rather idealised, Structural Health Monitoring (SHM) framework. The study is applied to a piezoelectric Lamb wave sensor network and is validated experimentally on a simple aluminium skin. The analytically-derived dispersion curves for Lamb wave propagation in aluminium are used in order to determine the wave velocities and thus their arrival time at given sensors. The Local Interaction Simulation Approach (LISA) is used to simulate the entire waveform propagation. Once the agreement between analytical, numerical and experimental data is verified on a baseline undamaged condition, the parametric LISA model has been iteratively run, varying the position and the length of a crack on an aluminium skin panel, generating the virtual experience necessary to train a supervised learning regressor based on Artificial Neural Networks (ANNs). After the algorithm structure has been statistically optimised, the network sensitivity to input variations has been evaluated on simulated signals through a technique inspired by information gap theory. Real Lamb wave signals are then processed into the algorithm, providing feasible real-time indication of damage characteristics.     

CAA broadband noise prediction for aeroacoustic design

The current status of a computational aeroacoustics (CAA) approach to simulate broadband noise is reviewed. The method rests on the use of steady Reynolds averaged Navier-Stokes (RANS) simulation to describe the time-averaged motion of turbulent flow. By means of synthetic turbulence the steady one-point statistics (e.g. turbulence kinetic energy) and turbulent length- and time-scales of RANS are translated into fluctuations having statistics that very accurately reproduce the initial RANS target-setting. The synthetic fluctuations are used to prescribe sound sources which drive linear perturbation equations. The whole approach represents a methodology to solve statistical noise theory with state-of-the-art CAA tools in the time-domain. A brief overview of the synthetic turbulence model and its numerical discretization in terms of the random particle-mesh (RPM) and fast random particle-mesh (FRPM) method is given. Results are presented for trailing-edge noise, slat noise, and jet noise. Some problems related to the formulation of vortex sound sources are discussed.