Structural Dynamic Identification Research Articles

Probabilistic approach for model and data uncertainties and its experimental identification in structural dynamics: Case of composite sandwich panels

This paper deals with the experimental identification and the validation of a non-parametric probabilistic approach allowing model uncertainties and data uncertainties to be taken into account in the numerical model developed to predict low- and medium-frequency dynamics of structures. The analysis is performed for a composite sandwich panel representing a complex dynamical system which is sufficiently simple to be completely described and which exhibits, not only data uncertainties, but above all model uncertainties. The dynamical identification is experimentally performed for eight panels. The experimental frequency response functions are used to identify the non-parametric probabilistic approach of model uncertainties. The prediction of the low- and medium-frequency dynamical responses obtained with the stochastic system is compared with the experimental measurements.

Parameter identification in explicit structural dynamics: performance of the extended Kalman filter

An extended Kalman filter (EKF) approach is adopted in this paper for structural systems subject to dynamic loadings to simultaneously estimate the state and calibrate constitutive parameters. To pursue this aim, after space and time discretizations a joint system state vector is introduced, gathering nodal displacements and constitutive parameters to be identified. Because of the linearization of the discretized equations governing filter updates, the EKF can lead to inaccurate model calibration. It is shown that, even though the state of the system is always followed with a high level of accuracy, unsatisfactory parameter estimations can be obtained in the case of degrading strength of the structure, that is in the case of softening. Both single degree-of-freedom (DOF) and multi-DOF dynamic systems are analyzed to detect the possible sources of this inaccuracy.

Electro-Mechanical Impedance Method for Crack Detection in Thin Plates

This paper describes the utilization of Electro-Mechanical (E/M) impedance method for structural health monitoring of thin plates. The method allows the direct identification of structural dynamics by obtaining its E/M impedance or admittance signatures. The analytical model for two-dimensional structure was developed and verified with experiments. Good matching of experimental results and calculated spectra was obtained for axial and flexural components. The ability of the method to identify the presence of damage was investigated by performing an experiment where the damage in the form of crack was simulated with an EDM slit placed at various distances from the sensor. It was found that the crack presence dramatically modifies the E/M impedance spectrum and this modification decreases as the distance between the sensor and the crack increases. Several overall-statistics damage metrics, which may be used for on-line structural heath monitoring, were investigated. Among these candidate damage metrics, the αth power of the correlation coefficient deviation, CCDα,3< α <7, used in the high frequency band 300-450 kHz, was found to be most successful. Careful selection of the high frequency band and proper choice of the appropriate damage metric were found to be essential for successful damage detection and structural health monitoring.

MIMO LMS-ARMAX IDENTIFICATION OF VIBRATING STRUCTURES—PART I: THE METHOD

A comprehensive linear multi stage autoregressive moving average with exogenous excitation (LMS-ARMAX) method for effective multiple-input multiple-output (MIMO) structural dynamics identification in the presence of noise is introduced. The method consists of (a) a vector ARMAX representation of an appropriate form, (b) effective LMS parameter estimation, (c) statistical order selection/validation, and (d) a digital dispersion analysis (DA) methodology for effective modal characterization. The LMS-ARMAX method overcomes many of the difficulties that had rendered MIMO ARMAX identification difficult in the past, featuring modest computational complexity, high accuracy, guaranteed algorithmic and model stability, and thus applicability to higher-dimensional problems and lightly damped structures, accurate modal parameter extraction, and effective distinction of structural from ‘extraneous’ modes. A critical assessment of the LMS-ARMAX method under various noise conditions, as well as comparisons with a simpler ARX version and the ERA (Eigensystem Realization Algorithm), are undertaken based upon experimental vibration data obtained from a scale aircraft skeleton structure. The paper is divided into two parts: The LMS-ARMAX method is presented in the first, and its critical assessment and comparisons in the second.

Identification of modal parameters, generalized and effective masses during base-driven tests

Structural dynamics identification is a common, long-standing procedure performed on large aerospace structures in order to investigate their dynamic behaviour. Usually, the experimental identification is accomplished by a set of single exciters placed at suitable structural points. An alternative to multiple point excitation is a driven-base test using a multi-axial shaker table. Multi-axis shaker facilities have been developed for experimental dynamic load simulation. However, they can be used for structural dynamics identification as well, whereby the overall structure is accelerated by the vibration table and the structural responses are measured. Based on these data, the structural dynamics of the structure can be identified. A common procedure for this identification is the determination of the modal paramaters, i.e., the eigenfrequencies, modal damping values, and mode shapes. A complete set of modal parameters requires the determination of the generalized mass as well. The measurement and evaluation of the interface forces between the structure and the multi-axial shaker facility makes the determination of the missing property possible. The present article develops the theoretical background for the identification and elucidates the experimental requirements. The application on a laboratory test structure as well as on two more complex structures is described. Typical measurement data and the extracted modal parameters are presented. The advantages and limitations of the test procedure are pointed out.

Determination of Modal Residues and Residual Flexibility for Time-Domain System Realization

A linear least-squares procedure for the determination of modal residues using time-domain system realization theory is presented. The present procedure is shown to be theoretically equivalent to residue determination in realization algorithms such as the Eigensystem Realization Algorithm (ERA) and Q-Markov COVER. However, isolating the optimal residue estimation problem from the general realization problem affords several advantages over standard realization algorithms for structural dynamics identification. Primary among these are the ability to identify data sets with large numbers of sensors using small numbers of reference point responses, and the inclusion of terms which accurately model the effects of residual flexibility. The accuracy and efficiency of the present realization theory-based procedure is demonstrated for both simulated and experimental data.

Neural network for structural dynamic model identification : H. M. Chen, G. Z. Qi, J. C. S. Yang & F. Amini, Journal of Engineering Mechanics — ASCE, 121(12), 1995, pp 1377–1381

Neural network for structural dynamic model identification : H. M. Chen, G. Z. Qi, J. C. S. Yang & F. Amini, Journal of Engineering Mechanics — ASCE, 121(12), 1995, pp 1377–1381

Neural Network for Structural Dynamic Model Identification

The identification and modeling of linear and nonlinear dynamic systems through the use of measured experimental data is a problem of considerable importance in engineering. Among the identification methods, the artificial neural network is a newly developed technique. Due to its attributes, such as parallelism, adaptability, robustness, and the inherent ability to handle nonlinearity, artificial neural networks have shown great promise in function mapping, pattern recognition, image processing, and so on. However, dynamic function mapping, including the structural dynamic model identification, is still a challenging topic in neural network applications. A neural network approach for structural dynamic model identification is presented in this paper. The neural network is trained, tested, and verified by using the responses recorded in a real apartment building during earthquakes. The results show that the dynamic behaviors of the building can be very well modeled by the trained neural network. The results also indicate the great potential of using neural networks in structural dynamic model identification.

Probabilistic Neural Network Approaches for Autonomous Identification of Structural Dynamics

This paper presents an application of Probabilistic Neural Networks (PNN) to identify dynamic responses of structures. The PNN architecture is described and its operation relative to other neural network types is discussed. The instant learning prop erty of the PNN is shown to be a critical advantage for applications where both adaptivity and autonomous operation are required. An example, PNN-based identification of struc tural responses from structural-member strain measurements is presented to illustrate op eration of the network. The network is shown to be capable of classifying dynamics in a spatial-frequency domain very quickly using a small number of active elements.

Optimal vibration control by the use of piezoceramic sensors and actuators

In this paper, a discrete degrees of freedom model has been formulated for a structural dynamic system consisting of a linear elastic structure, bonded piezoceramic sensors and actuators, and a feedback signal conditioning system. In addition, an optimal control procedure based on the minimization of a quadratic performance index of state and control vectors has been developed that uses output feedback methods. Finally, the application of the model and the control technique has been demonstrated through the example of a linear elastic beam with piezoceramic sensors and actuators occupying discrete subdomains of the beam upper and lower surfaces. A model for the linear elastic beam has been obtained by using test results and a structural dynamic system identification method based on an equation error approach. Results for various weights in the performance index are included, and implications for future applications are discussed. N the past few years, there has been considerable research activity in the field of active and passive control of vibra- tions of flexible structures. One of the methods of active con- trol of vibrations, termed electronic damping in some of the early literature,1'6 involves the placement of piezoceramic devices on a structure to sense and control dynamic strains induced by structural vibrations. The deformation of a sens- ing transducer results in an electrical current that is condi- tioned by operations such as amplification and shifting of the phase of the signal. The conditioned signal is then applied to another piezoceramic, electrostrictive, or magnetostrictive device placed at a selected location on the structure. This trans- ducer acts as an actuator and transmits mechanical energy to the structure. Depending on the applied voltage, electrome- chanical coupling of the forcing transducer to the structure, and the location of the transducers, a degree of vibration control of flexible structures can be achieved. To date, applica- tions of the aforementioned scheme have primarily been in the area of large space structures, such as in the work of Crawley and Deluis,7 but the scheme is applicable to any structure with lightweight components. This type of active control offers unique features that are not usually employed for control of structural vibrations. The dynamics of direct contact type sensors and actuators permit a wide frequency range of control. A measure of tunability is provided for the control of structural systems that age or grow. Finally, this method adds little mass to the controlled flexible structure so that the existing plant model does not need to be modified to account for the mass of the transducers. To utilize the advantages of piezoceramic transducers, it is necessary to select appropriate positions of the transducers and to select the sensor signals that are to be fed back to the actuators. The problem of selecting the locations of the transducers is a complete problem in itself and thus will not be addressed in this paper. There has been some work in

Suboptimum Maximum Likelihood Estimation of Structural Parameters from Multiple-Excitation Vibration Data

In this paper an effective stochastic and multiple-excitation single-response approach to structural dynamics identification is introduced. The proposed approach accounts for many previously unaccounted for aspects of the problem, as it is based on: A proper, special-form, scalar ARMAX-type representation of the structural and noise dynamics; a new Suboptimum Maximum Likelihood (SML) discrete estimation algorithm (Fassois and Lee, 1990); systematic and efficient modeling strategy and model validation procedures; as well as accurate modal parameter extraction that is compatible with the employed model structure and excitation signal forms. In addition to its comprehensiveness, the proposed approach overcomes the well-known limitations of deterministic time-domain methods in dealing with noise-corrupted data records, while also circumventing some of the major difficulties of existing stochastic schemes by featuring guaranteed algorithmic stability, elimination of wrong convergence problems, very modest computational complexity, and minimal operator intervention. The effectiveness of the approach is verified through numerical simulations with noise-corrupted vibration data, and structural systems characterized by well-separated and closely-spaced vibrational modes. Comparisons with the classical Frequency Domain Method (FDM) are also made, and the approach’s advantages over deterministic methods are demonstrated through comparisons with the Eigensystem Realization Algorithm (ERA). Experimental results, where the proposed approach is used for the modal analysis of a flexible beam from laboratory data, are also presented.

Recursive Identification of Vibrating Structures from Noise-Corrupted Observations, Part 1: Identification Approaches

In this paper the problem of recursive structural dynamics identification from noise-corrupted observations is addressed, and approaches that overcome the weaknesses of current methods, stemming from their underlying deterministic nature and ignorance of the fact that structural systems are inherently continuous-time, are introduced. Towards this end the problem is imbedded into a stochastic framework within which the inadequacy of standard Recursive Least Squares-based approaches is demonstrated. The fact that the continuous-time nature of structural systems necessitates the use of compatible triples of excitation signal type, model structure, and discrete-to-continuous transformation for modal parameter extraction is shown, and two such triples constructed. Based on these, as well as a new stochastic recursive estimation algorithm referred to as Recursive Filtered Least Squares (RFLS) and two other available schemes, a number of structural dynamics identification approaches are formulated and their performance characteristics evaluated. For this purpose structural systems with both well separated and closely spaced modes are used, and emphasis is placed on issues such as the achievable accuracy and resolution, rate of convergence, noise rejection, and computational complexity. The paper is divided into two parts: The problem formulation, the study of the interrelationships among excitation signal type, model structure, and discrete-to-continuous transformation, as well as the formulation of the stochastic identification approaches are presented in the first part, whereas a critical evaluation of their performance characteristics based on both simulated and experimental data is presented in the second.

Recursive Identification of Vibrating Structures from Noise-Corrupted Observations, Part 2: Performance Evaluation via Numerical and Laboratory Experiments

In the first part of this paper (Ben Mrad and Fassois, 1991), the problem of recursive structural dynamics identification from noise-corrupted observations was examined, and six approaches that properly account for the presence of noise in the experimental data and the fact that structural systems are inherently continuous-time were formulated. In this second part the relative performance characteristics of these approaches are investigated by using numerically simulated and laboratory data, the latter obtained from a free-free beam experiment. Structural systems with well separated and closely spaced modes are considered, and emphasis is placed on issues such as the achievable accuracy and resolution, rate of convergence, noise rejection, computational complexity, the need for model overdetermination, and the distinction of structural from “computational” vibrational modes. Unlike alternative methods, when properly used, the proposed approaches are shown to offer good performance with data corrupted at various noise-to-signal ratios.

A Linear Time-Domain Method for Structural Dynamics Identification

A two-stage, time-domain structural dynamics identification method, that circumvents some of the main drawbacks of current techniques, and combines good noise rejection properties with a low computational load and accurate modal parameter extraction, is proposed. In the first stage of the method a discrete model is obtained through a linear estimation scheme and a systematic and effective modeling strategy. In the second stage the modal parameters are evaluated according to a new procedure that is capable of detecting and correcting large errors that may be introduced into the modal parameter estimates through the discrete-to-continuous transformation. The proposed method yields consistent modal parameter estimates at a low computational load, and is well-suited for microcomputer implementation. Its effectiveness is finally demonstrated with both simulated and actual experimental data.

Adaptive Modeling, Identification, and Control of Dynamic Structural Systems. II: Applications

Recently developed adaptive methods for modeling, identification, and control are now being successfully used in various branches of science and engineering. These methods present significant advantages over the classical methods, e.g., they can remove the noise from the signal over the whole frequency band, they can track time‐varying characteristics of systems, and they make it possible to control unknown systems. In this paper, five examples for the application of adaptive modeling, identification, and control techniques in structural dynamics are presented. The examples are as follows: (1) Identification of a time‐varying simulated system; (2) identification of a building with soil‐structure interaction by using earthquake vibration recordings; (3) identification of a building with nonlinear vibrations by using earthquake vibration recordings; (4) adaptive control of a simulated system; and (5) adaptive control of ambient vibrations of a building. Prior to examples, methods for preprocessing the data are outlined. The paper is the second of two companion papers. The theory pertinent to examples is given in the first paper.

A Unified Theory of Recursive, Frequency Domain Filters With Application to System Identification in Structural Dynamics

In this paper a unified theory is presented for system identification in structural dynamics using recursive frequency-domain filters. Output error, equation error, and instrumental variable (I. V.) filters are developed as special cases. Parameter estimates are extracted from noisy simulated data from a multi-degree-of-freedom system. The equation error filter is strongly convergent but is prone to asymptotic bias error in the presence of measurement noise. An I. V. filter is developed in order to overcome the bias problem while maintaining the desirable convergence properties of the equation error approach.

Studies on identification of structural dynamics. Survey of current works and proposal of a new approach.

Studies on identification of structural dynamics. Survey of current works and proposal of a new approach.

Experimental evaluation of flexible structure identification using lattice filters

This paper presents the use of least square lattice filters in identification of the dynamics of highly flexible structures. Lattice filters have been used extensively in the areas of adaptive signal processing and speech synthesis. Herein, they are used for on-line identification of the number of modes, mode shapes and modal amplitude time series from the measurement data of flexible structures. The theory is illustrated using experimental data for a simple free-free beam and a more complex flexible, two-dimensional grid apparatus. Results presented indicate that the lattice filter approach produces effective identification of structural dynamics for the class of structures studied to this time.

Experimental Evaluation of Flexible Structure Identification using Lattice Filters

This paper presents the use of least square lattice filters in identification of the dynamics of highly flexible structures. Lattice filters have been used extensively in the areas of adaptive signal processing and speech synthesis. Herein, they are used for on-line identification of the number of modes, mode shapes and modal amplitude time series from the measurement data. The theory is illustrated using experimental data for a simple free-free beam and a more complex, flexible, two-dimensional grid apparatus. Results presented indicate that the lattice filter approach produces effective identification of structural dynamics for the class of structures studied to this time.

Analysis of Structural Nonstationary Behaviour and Dynamic System Identification Based on the Auto-Regressive Model Fitting

Analysis of Structural Nonstationary Behaviour and Dynamic System Identification Based on the Auto-Regressive Model Fitting