Structural Dynamic Identification Research Articles

Structural dynamic nonlinear model and parameter identification based on the stiffness and damping marginal curves

This paper presents a novel structural dynamic nonlinear model and parameter identification method based on the stiffness and damping marginal curves. The stiffness and damping marginal curves are first extracted from the structural dynamic responses. Then, nine nonlinear feature indices (NFIs) are defined based on the marginal curves to describe the characteristics of various nonlinear models. To reduce the dimension of NFIs and facilitate the subsequent calculation of the support vector machine (SVM), the principal component analysis (PCA) is implemented. Afterwards, the NFIs processed by PCA are employed as the training samples to SVM classifier, which is used to identify the structural nonlinear model. According to the identified nonlinear model corresponding to the type of nonlinearity, the parameters of the nonlinear model are further identified by the nonlinear least square method. The numerical results of a single degree of freedom (SDOF) system and a cantilever beam structure demonstrate that the proposed method can effectively identify both nonlinear model and corresponding parameters under various excitations even considering the noise effect. Subsequently, the proposed method is also verified by a benchmark system subjected to a semisinusoidal pulse load and a beam bridge structure subjected to an earthquake load. The proposed method is also applied to the experimental test of a bolted joint cantilever beam subjected to a random excitation in the laboratory. Both numerical and test results demonstrate that the proposed method can identify both nonlinear model and corresponding parameters within good accuracy and robustness.

A new hybrid conjugate gradient method for dynamic force reconstruction

A new hybrid conjugate gradient method is proposed in this article based on the gradient operator and applied to the structural dynamic load identification problem. It has proved that the present method with the strong Wolfe line search possesses sufficient descent property. In addition, the present method is globally convergent when the parameter in the strong Wolfe line search conditions is restricted in some suitable intervals. Three example problems from engineering are solved by the newly developed conjugate gradient method to demonstrate the robustness and effectiveness of conjugate gradient method in solving multi-source dynamic load identification problems. Compared with the traditional Landweber iteration regularization method (Landweber), the proposed conjugate gradient method can more stably and effectively overcome the influences of noise, largely reduce the number of iterations, and provide accurate results in identifying multi-source dynamic force in practical engineering structure.

Parametric vibration source characterization of a reaction-wheel-assembly by evaluation on predictions of blocked forces and simple receiver responses

This study is to present a parametric characterization of reaction wheel assembly (RWA) as a vibration source for quantitative prediction of operational vibrations of a receiver on which the RWA is to be installed. The parametric source characterization proposed in this paper is based on measurements of blocked forces and torques at all frequencies in a band rather than only at harmonic frequencies for each operation speed. It includes identification of structural dynamics of the RWA itself as well as source force characteristics from measurements of the blocked forces and torques. Validation of the parametric modeling of the RWA is done based on the closeness or coherence between the measurements of the power spectral density functions of the blocked forces and torques and their predictions by modeling. Additional evaluation is proposed to enhance prediction capability of the parametric model for the operational vibrations by comparing the predicted responses of a simple cantilever with measurements during actual operations of the RWA on the cantilever.

A framework for the identification of full-field structural dynamics using sequences of images in the presence of non-ideal operating conditions

Recent developments in the ability to automatically and efficiently extract natural frequencies, damping ratios, and full-field mode shapes from video of vibrating structures has great potential for reducing the resources and time required for performing experimental and operational modal analysis at very high spatial resolution. Furthermore, these techniques have the added advantage that they can be implemented remotely and in a non-contact fashion. Emerging full-field imaging techniques therefore have potential to allow the identification of the modal properties of structures in regimes that used to be challenging. For instance, these techniques suggest that the high spatial resolution structural identification could be performed on an aircraft during flight using a ground or aircraft-based imager. They also have the potential to identify the dynamics of microscopic systems. In order to realize this capability it will be necessary to develop techniques that can extract full-field structural dynamics in the presence of non-ideal operating conditions. In this work, we develop a framework for the deployment of emerging algorithms that allow the automatic extraction of high-resolution, full-field modal parameters in the presence of non-ideal operating conditions. One of the most notable non-ideal operating conditions is the rigid body motion of both the structure being measured as well as the imager performing the measurement. We demonstrate an instantiation of the framework by showing how it can be used to address, in-plane, translational, rigid body motion. The development of a frame-to-frame keypoint–based technique for identifying full-field structural dynamics in the presence of either rigid body motion is presented and demonstrated in the context of the framework for the deployment of full-field structural identification techniques in the presence of non-ideal operating conditions. It is expected that this framework will ultimately help enable the collection of full-field structural dynamics using measurement platforms including unmanned aerial vehicles, robotic telescopes, satellites, imagers mounted in high-vibration environments (seismic, industrial, harsh weather), characterization of microscopic structures, and human-carried imagers. If imager-based structural identification techniques mature to the point that they can be used in non-ideal field conditions, it could open up the possibility that the structural health monitoring community will be able to think beyond monitoring individual structures, to full-field structural integrity monitoring at the city scale.

Seismic Behaviour of Sheathed CFS Buildings: Shake-Table Testing and Numerical Modelling

In the past, the effort of the research was focused on the characterization and modelling of isolated CFS members or parts of building, but this cannot be enough for innovative structure, in which the sheathing panels interact with the steel framing providing the bracing effects against seismic actions. Therefore, in order to evaluate the seismic behaviour of CFS buildings sheathed with gypsum panels, a wide experimental campaign was conducted at University of Naples “Federico II” in the framework of European research project ELISSA (Energy efficient LIghtweight-Sustainable-SAfe steel construction). In particular, a two-storey building was tested on the shaking-table, considering different construction phases. In the first phase, the building included only structural elements and dynamic identification tests were carried out, whereas, in the second phase, the building was completed with all finishing components and it was tested for dynamic identification and under natural ground motions. In addition, a numerical model able to simulate the dynamic/earthquake response of the whole building, considering also the effect of finishing materials, was developed in OpenSees environment. The present paper describes the main results of shake-table testing and numerical modelling.

Validation of time-delayed recursive force identification in structural dynamics

This paper presents a validation of a smoothing algorithm for joint input-state estimation using data obtained from a full-scale experiment on a footbridge. A dynamic model of the footbridge is obtained using a detailed finite element model that is calibrated using the natural frequencies and mode shapes obtained from an operational modal analysis. The smoothing algorithm is used for the identification of two impact forces applied to the bridge deck. The validation involves comparing the estimated forces with the actual, measured forces. When the response measurements are not collocated with the estimated forces, the assumption of a time delay for recursive estimation allows to significantly reduce the estimation uncertainty as compared to filtering.

A new, challenging benchmark for nonlinear system identification

The progress accomplished during the past decade in nonlinear system identification in structural dynamics is considerable. The objective of the present paper is to consolidate this progress by challenging the community through a new benchmark structure exhibiting complex nonlinear dynamics. The proposed structure consists of two offset cantilevered beams connected by a highly flexible element. For increasing forcing amplitudes, the system sequentially features linear behaviour, localised nonlinearity associated with the buckling of the connecting element, and distributed nonlinearity resulting from large elastic deformations across the structure. A finite element-based code with time integration capabilities is made available at https://sem.org/nonlinear-systems-imac-focus-group/. This code permits the numerical simulation of the benchmark dynamics in response to arbitrary excitation signals.

Nonlinear system identification in structural dynamics: 10 more years of progress

Nonlinear system identification is a vast research field, today attracting a great deal of attention in the structural dynamics community. Ten years ago, an MSSP paper reviewing the progress achieved until then [1] concluded that the identification of simple continuous structures with localised nonlinearities was within reach. The past decade witnessed a shift in emphasis, accommodating the growing industrial need for a first generation of tools capable of addressing complex nonlinearities in larger-scale structures. The objective of the present paper is to survey the key developments which arose in the field since 2006, and to illustrate state-of-the-art techniques using a real-world satellite structure. Finally, a broader perspective to nonlinear system identification is provided by discussing the central role played by experimental models in the design cycle of engineering structures.

Time‐domain Galerkin method for dynamic load identification

SummaryThis paper proposes a new method called time‐domain Galerkin method (TDGM) for investigating the structural dynamic load identification problems. Firstly, the shape functions are adopted to approximate three parameters, such as the dynamic load, kernel function response, and measured structural response Secondly, defining a residual function could be expressed as the difference of the measured response and the computational response. Thirdly, select an appropriate weighting function to multiply the defined residual function and make integral operation with respect to time to be zero. Finally, when the shape functions are chosen as the weighting function, it establishes the forward model called TDGM. Furthermore, the regularization method could have effectiveness in solving the ill‐posed matrix of load reconstruction and obtaining the accurate identified results of the dynamic load. Compared with the traditional Green kernel function method (GKFM), TDGM can effectively overcome the influences of noise and improve the accuracy of the dynamic load identification. Three numerical examples are provided to demonstrate the correctness and advantages of TDGM. Copyright © 2015 John Wiley & Sons, Ltd.

Stable force identification in structural dynamics using Kalman filtering and dummy-measurements

Many engineering applications require the knowledge of input forces to mechanical systems. However, in practice, it is quite difficult to measure these forces directly. In order to obtain an estimate of the input forces to structural systems, Kalman filtering based techniques have recently been introduced. These state-estimation techniques allow estimating the forces concurrent with the states of a system, based on a limited number of measurements. In practice, acceleration measurements are most convenient to use in structural dynamics applications. This paper proposes an analytical analysis of the stability of the Kalman based force estimation techniques and shows that only using acceleration measurements inherently leads to unreliable results. In order to circumvent this issue, the addition of dummy-measurements on a position level is proposed. These fictitious measurements dictate the estimator to return to an undeformed state and lead to a stable estimation approach. The proposed method is validated through both a numerical and a practical experiment. Both experiments show the inadequacy of the augmented Kalman filter based on only acceleration measurements to provide stable results. The estimator with dummy measurements on the other hand provides good results in the case of an unbiased external load.

Structural dynamic identification of a damaged and restored masonry vault using Ambient Vibrations

In this study, the dynamic characteristics of the masonry vault of Küçük Fatih Mosque have been identified by using Ambient Vibration Test. The vault was damaged and then restored. The mosque is located in the Bahçecik Quarter of Trabzon in Turkey, and it was registered as immovable cultural property. The mosque was restored by the local Regional Directorate of Foundations in 2012. The mosque has a vault which is supported by three masonry arches. At the beginning of the restoration, any damage was not observed on the vault. After the dismantling of the plaster, some cracks appeared on the masonry arches under the vault. Before the repairing of the vault, the dynamic behavior was determined by measuring the vibrational responses of the vault under environmental effects such as wind and traffic, the natural frequencies, mode shapes and the modal damping ratios were identified. The repairing project of the damaged vault was prepared and applied by skillful members. After the repairing of the vault, the vibration test was repeated and the dynamic characteristics of the vault were determined. It was observed that the first five natural frequency values of the vault are increased and the damping ratios were changed irregularly. The first two modal behaviors were obtained to be quite similar and the others were different.

Identification, Model Updating, and Validation of a Steel Twin Deck Curved Cable‐Stayed Footbridge

AbstractTo perform a realistic reliability analysis of a complex cable‐stayed steel footbridge subject to natural hazard and corrosion, this article addresses a rational process of modeling and simulation based on identification, model updating, and validation. In particular, the object of this study is the Ponte del Mare footbridge located in Pescara, Italy; this bridge was selected as being a complex twin deck curved footbridge because it is prone to corrosion by the aggressive marine environment. With the modeling and simulation objectives in mind, a preliminary finite element (FE) model was realized using the ANSYS software. However, uncertainties in FE modeling and changes during its construction suggested the use of experimental system identification. As a result, the sensor location was supported by a preliminary FE model of the footbridge, although to discriminate close modes of the footbridge and locate identification sensor layouts, Auto Modal Assurance Criterion (AutoMAC) values and stabilization diagram techniques were adopted. Modal characteristics of the footbridge were extracted from signals produced by ambient vibration via the stochastic subspace identification (SSI) algorithm, although similar quantities were identified with free‐decay signals produced by impulse excitation using the ERA algorithm. All these procedures were implemented in the Structural Dynamic Identification Toolbox (SDIT) code developed in a MATLAB environment. The discrepancies between analytical and experimental frequencies led to a first update of the FE model based on Powell's dog‐leg method that relied on a trust‐region approach. As a result, the identified FE model was capable of reproducing the response of the footbridge subject to realistic gravity and wind load conditions. Finally, the FE was further updated in the modal domain, by changing both the stationary aerodynamic coefficients and the flutter derivatives of deck sections to take into account the effects of the curved deck layout.

A local approach for the LPV identification of an actuated beam using piezoelectric actuators and sensors

This paper considers the identification of structural dynamics by identifying its frequency response functions (FRFs) – a mathematical representation of the relationship between the vibration response at one location and excitation at the same or another location. The spatially-varying characteristics of the FRFs at various input and output locations are explored, and lead to a spatial linear parameter varying (LPV) representation. A local LPV identification technique for lumped systems is adapted here to spatially-interconnected systems. The identification of a spatial LPV model facilitates the experimental work, and also simplifies the controller synthesis. The proposed approach is applied to identify an actuated beam equipped with an array of collocated piezoelectric actuators and sensors for performance illustration.

Modal identification of structures by a novel approach based on FDD-wavelet method

An important application of system identification in structural dynamics is the determination of natural frequencies, mode shapes and damping ratios during operation which can then be used for calibrating numerical models. In this paper, the combination of two advanced methods of Operational Modal Analysis (OMA) called Frequency Domain Decomposition (FDD) and Continuous Wavelet Transform (CWT) based on novel cyclic averaging of correlation functions (CACF) technique are used for identification of dynamic properties. By using this technique, the autocorrelation of averaged correlation functions is used instead of original signals. Integration of FDD and CWT methods is used to overcome their deficiency and take advantage of the unique capabilities of these methods. The FDD method is able to accurately estimate the natural frequencies and mode shapes of structures in the frequency domain. On the other hand, the CWT method is in the time-frequency domain for decomposition of a signal at different frequencies and determines the damping coefficients. In this paper, a new formulation applied to the wavelet transform of the averaged correlation function of an ambient response is proposed. This application causes to accurate estimation of damping ratios from weak (noise) or strong (earthquake) vibrations and long or short duration record. For this purpose, the modified Morlet wavelet having two free parameters is used. The optimum values of these two parameters are obtained by employing a technique which minimizes the entropy of the wavelet coefficients matrix. The capabilities of the novel FDD-Wavelet method in the system identification of various dynamic systems with regular or irregular distribution of mass and stiffness are illustrated. This combined approach is superior to classic methods and yields results that agree well with the exact solutions of the numerical models.

Dynamic Load Identification Theoretical Summary and the Application on Mining Machinery

This paper is devoted to describe a new dynamic load identification method about mining machinery structural; Frist, reviews the background of structural dynamic load identification theory; Then, introduce some familiar dynamic load identification methods, including frequency domain method, time domain method and some other new methods; Describe the steps about dynamic load identification method used in mining machinery engineering structures; Last, practice shows that the method is profitable.

Parameter estimation and model selection for a class of hysteretic systems using Bayesian inference

The aim of this paper is to provide an overview of the possible advantages of adopting a Bayesian approach to nonlinear system identification in structural dynamics. In contrast to identification schemes which estimate maximum likelihood values (or other point estimates) for parameters, the Bayesian scheme discussed here provides information about the complete probability density functions of parameter estimates without adopting restrictive assumptions about their nature. Among other advantages of the Bayesian viewpoint are the abilities to make informed decisions about model selection and also to effectively make predictions over entire classes of models, with each individual model weighted according to its ability to explain the observed data.The approach is illustrated using data from simulated systems, first a Duffing oscillator and then a new application to hysteretic system of the Bouc–Wen type. The modelling and identification of the latter type of system has long presented problems due to the fact that commonly used model structures like the Bouc–Wen model are nonlinear in the parameters, or have unmeasured states, etc. These issues have been dealt with in the past by adopting an optimisation-based approach to the problem; in particular, the differential evolution algorithm has proved very effective. An objective of the current paper is to illustrate how the Bayesian approach provides the same information and more as the optimisation approach; it yields parameter estimates and their associated confidence intervals, but can also provide confidence bounds on model predictions and evidence measures which can be used to select the most appropriate model from a candidate set. A new model selection criterion in this context – the Deviance Information Criterion (DIC) – is presented here.

An augmented Kalman filter for force identification in structural dynamics

An augmented Kalman filter for force identification in structural dynamics is developed, in which the unknown forces are included in the state vector and estimated in conjunction with the states. Noise is modeled as a stochastic process and is assumed to be present not only on the measurements, but also on the state variables, thus accounting to some extent for modeling errors. This distinguishes the proposed technique from purely deterministic methods for force identification in which no errors are assumed on the states. To analyze the effect hereof on the quality of the identification, the results obtained with a commonly used recursive least-squares method, the Dynamic Programming algorithm, are compared to those obtained using the augmented filter in a laboratory experiment on an instrumented steel beam. It is shown how, in the collocated case, more accurate results can be obtained with the augmented filter due to its incorporation of modeling errors. In the non-collocated case, however, better solutions are produced by classical deterministic methods as Dynamic Programming in which only the forces are estimated, and not the states as well.

Structural parameters and dynamic loading identification from incomplete measurements: Approach and validation

System identification is becoming more important in structural dynamic applications including structural model update, damage detection primarily due to the rapid increase in the number of damaged or deteriorated engineering structures, and load identification for remaining service life forecasting. Time-domain identification techniques based on measured vibration data, e.g. the least-squares estimation (LSE), have been studied for a relatively long time and shown to be useful. However, the traditional least-squares techniques require that all the external excitation measurements should be available, which may not be the case for many practical applications. In this paper, by introducing a weighted positive definite matrix to the objective function and a learning coefficient using the information in the previous iterations in the identification approach to improve the convergence performance, an alternative iterative approach for both structural parameters and dynamic loading identification, referred to as weighted adaptive iterative least-squares estimation with incomplete measured excitations (WAILSE-IME), was proposed. The accuracy, convergence, and robustness of the proposed approach was demonstrated via numerical simulation on a six-story shear building model with noise-free and different levels of noise-polluted structural dynamic response measurements. The effects of the positive weight matrix, the learning coefficient, and the sampling duration on the convergence and the accuracy of the proposed approach were discussed and the results were compared with available related literature results. Results show that the proposed approach can simultaneously identify structural parameters and unknown excitations within very limited iterations with high accuracy and shows its robustness even noise-polluted dynamic response measurements are utilized. Furthermore, the approach was validated via available experimental measurements for a four-story frame structure excited by impact excitations. The results show that the proposed approach is capable of identifying both structural parameters and the unmeasured excitations with acceptable accuracy and improved convergence.

Magneto-mechanical impedance identification and diagnosis of metallic structures

Magneto-mechanical impedance (MMI) method is implemented for multi-modal structural dynamic identification and diagnosis of metallic structures. Active elements of the method, magneto-elastic active sensors (MEAS), consist of an electrical coil and a permanent magnet facilitating electromagnetic generation and reception of elastic waves via the eddy current mechanism. The paper describes experimental arrangements and proof-of-concept experiments demonstrating availability of structural dynamic features in the MMI response and feasibility of MMI measurements for nondestructive assessment of structural condition. An analytical model describing MMI response of one-dimensional non-ferromagnetic structure is presented. The model includes three distinct contributions: dynamics of the structural element, electromagnetic coupling, and sensor characteristics. Different excitation models for MEAS were considered that account for spatial distribution of the structural load. Effects of structural parameters and sensor characteristic on the MMI signature are investigated and several approaches for improving MMI measurements are suggested. The paper presents examples of MMI monitoring of simple and complex structures. In the reported investigations, MMI spectral features, such as spectral amplitude, frequency shift and redistribution of impedance peaks are explored for structural damage detection and characterization. It is suggested that MMI may facilitate structural diagnostics requiring either embeddable sensors or non-contact transducers.

Nonlinear identification in structural dynamics based on Wiener series and Kautz filters

The present paper proposes a method to identify localized nonlinear parameters in structural dynamics using vibration data. The approach is based on the identification of the first and second-order Volterra kernels in an orthogonal basis, namely Wiener kernels, while taking the experimental data as exact values. The focus is to identify an already localized nonlinearity with known structure. An optimization procedure is implemented using a metric involving the difference between the experimental kernel and the simulated orthogonal kernel from model updating, which is function of the unknown nonlinear parameters. In order to reduce the problems of convergence, the Kautz filter is used to decrease the number of samples to estimate. The proposed methodology is illustrated on a numerical example using a cantilever beam and its advantages and drawbacks are discussed in detail.