Structural Dynamic Identification Research Articles

Low frequency load identification under high noise level using weighted total least squares

Load identification in structural dynamics is an ill-conditioned inverse problem, and the errors exist in both the transfer function matrix and the response vector, which have a great influence on the accuracy of the identification, especially at the low frequency and high noise. Although the Total Least Squares (TLS) method can consider the errors in the transfer function matrix and the response vector, the problem of unequal precision between them has not been properly solved. In this article, the Weighted Total Least Squares (WTLS) method for load identification is presented. First, the variance–covariance matrices are constructed using stochastic information, which can consider the unequal precision of the data and make the solution less biased and more precise. Then, Tikhonov regularization is used to regularize the WTLS method to reduce the ill-condition of the transfer function matrix. To validate the performance of the WTLS method under different noise levels, a load identification simulation with four excitation loads on a plate and a load identification experiment with three excitation loads on a steel plate were studied. The results show that when the noise levels of the transfer function and the response are different, the accuracy of the TLS solution is poor. Especially when the noise levels are high, the identification deviations are large. The WTLS method considers the unequal noise levels using the weight matrices, which provides more stable load estimates at different noise levels. And the identification deviations are greatly reduced compared to the TLS method.

Sparse Bayesian machine learning for the interpretable identification of nonlinear structural dynamics: Towards the experimental data-driven discovery of a quasi zero stiffness device

Data-driven discovery of governing laws for complex nonlinear structural dynamic systems remains a challenging issue of paramount importance. This work addresses the above issue by leveraging the available noisy data and integrating sparse Bayesian machine learning (ML) techniques to discover the governing equations. The problem of discovery is re-cast as the automatic relevance determination of models (model selection) from the library of potential candidate basis terms and their coefficients are determined (parameter identification) using sparse Bayesian linear regression. Two sparsity promoting ML algorithms based on relevance vector machines have been employed. Both these approaches use Bayesian statistics and quantify the uncertainty associated with the model predictions. Results from four representative numerical examples of nonlinear structural dynamics illustrate excellent performance of both proposed approaches. The results have been validated with the true governing equations and time response data. Comparison has also been made with a recent and popular sparse discovery approach. Finally, the proposed framework is applied to real datasets that were generated from an in-house designed experimental setup of a quasi zero stiffness device and good performance has been observed.

The Least Squares Time Element Method Based on Wavelet Approximation for Structural Dynamic Load Identification

Dynamic load identification is a commonly used and quite important approach to obtain the excitation loads of structures in engineering practice. In this paper, a novel dynamic load identification method combining the least squares time element method (LSTEM), wavelet scaling function and regularization method is proposed, which performs a better accuracy and a stronger anti-noise ability. It decomposes the time history of dynamic load into a series of time elements, and approximates the load profile at each time element using wavelet scaling functions. In order to balance the accuracy and efficiency for load identification, an optimal wavelet resolution is then determined. Simultaneously, the least squares time element model is derived which establishes the forward model for computing the wavelet coefficient. Finally, the wavelet coefficients for dynamic load identification are accurately and stably solved by implementing regularization. By this method, on the one hand, the wavelet scaling function and LSTEM improve the identification accuracy, and on the other hand, the integral process in the least squares operation gains the anti-noise ability for the load identification. A numerical example of a roof structure and an experiment of a composite laminate are studied and verify the effectiveness of the proposed method.

Parameter design and performance evaluation of tuned mass damper (TMD) for seismic control of structure considering soil-structure interaction (SSI)

Tuned mass damper (TMD) is a practical tool for reducing structural vibration. The current TMD design often use the dynamic characteristics of structures with fixed base. However, in terms of resisting earthquakes especially when the soil-structure interaction (SSI) effect is prominent, the TMD designed for the fixed base situation behaves unfavorably and even amplifies the structural response. In this paper, a parameter design and performance evaluation of TMD for seismic control of structure considering SSI is studied. The contents include the SSI modeling, structural dynamic characteristic identification, and TMD parameter designing. A seismic SSI model that the soil is simulated by an accurate lumped parameter models (LPMs) is built firstly. A simple and practical method is then used to identify the structural dynamic characteristic of SSI model. The identified structural frequency is used to compute the parameters of TMD. Finally, two types of structures, three kinds of soils, and 100 ground motions are applied to comprehensively evaluate the TMD performance through the comparison with the fixed-ground-based design and optimization-algorithm-based design. The research shows the TMD designed by the proposed method can show a good performance and robustness.

Identification and mechanistic exploration of structural and conformational dynamics of NF-kB inhibitors: rationale insights from in silico and in vitro studies

Increased expression of target genes that code for proinflammatory chemical mediators results from a series of intracellular cascades triggered by activation of dysregulated NF-κB signaling pathway. Dysfunctional NF-kB signaling amplifies and perpetuates autoimmune responses in inflammatory diseases, including psoriasis. This study aimed to identify therapeutically relevant NF-kB inhibitors and elucidate the mechanistic aspects behind NF-kB inhibition. After virtual screening and molecular docking, five hit NF-kB inhibitors opted, and their therapeutic efficacy was examined using cell-based assays in TNF-α stimulated human keratinocyte cells. To investigate the conformational changes of target protein and inhibitor-protein interaction mechanisms, molecular dynamics (MD) simulations, binding free energy calculations together with principal component (PC) analysis, dynamics cross-correlation matrix analysis (DCCM), free energy landscape (FEL) analysis and quantum mechanical calculations were carried out. Among identified NF-kB inhibitors, myricetin and hesperidin significantly scavenged intracellular ROS and inhibited NF-kB activation. Analysis of the MD simulation trajectories of ligand–protein complexes revealed that myricetin and hesperidin formed energetically stabilized complexes with the target protein and were able to lock NF-kB in a closed conformation. Myricetin and hesperidin binding to the target protein significantly impacted conformational changes and internal dynamics of amino acid residues in protein domains. Tyr57, Glu60, Lys144 and Asp239 residues majorly contributed to locking the NF-kB in a closed conformation. The combinatorial approach employing in silico tools integrated with cell-based approaches substantiated the binding mechanism and NF-kB active site inhibition by the lead molecule myricetin, which can be explored as a viable antipsoriatic drug candidate associated with dysregulated NF-kB. Communicated by Ramaswamy H. Sarma

A new OMA method to perform structural dynamic identification: numerical and experimental investigation

Operational modal analysis (OMA) methods are nowadays common in civil, mechanical and aerospace engineering to identify and monitor structural systems without any knowledge on the structural excitation provided that the latter is due to ambient vibrations. For this reason, OMA methods are embedded with stochastic concepts and then it is difficult for users that have no-knowledge in signal analysis and stochastic dynamics. In this paper an innovative method useful for structural health monitoring (SHM) is proposed. It is based on the signal filtering and on the Hilbert transform of the correlation function matrix. Specifically, the modal shapes are estimated from the correlation functions matrix of the filtered output process and then the frequencies and the damping ratios are estimated from the analytical signals of the mono-component correlation functions: a complex signals in which the real part represents the correlation function and the imaginary part is its Hilbert transform. This method is very simple to use since requires only few interactions with the users and thus it can be used also from users that are not experts in the aforementioned areas. In order to prove the reliability of the proposed method, numerical simulations and experimental tests are reported also considering comparisons with the most popular OMA methods.

Structural Health Monitoring and Dynamic Identification of the Historical Town-Hall of Borgo Val di Taro

A good structural knowledge of heritage buildings is a key factor for their conservation and for the planning of retrofit interventions, especially in high seismic risk areas, like Italy. Within this context, structural health monitoring techniques, like those based on ambient vibrations under operating conditions, represent powerful tools for evaluating the dynamic behavior of existing structures. The presented methodology is particularly interesting for historic and monumental buildings due to its non-invasiveness. This work illustrates the installation of a monitoring system in the historical masonry Town-Hall of Borgo Val di Taro, dating back to the fifteen century, for its ambient vibration modal identification. The so collected data are then used for the construction of a refined numerical model for the simulation of the dynamic response of the building, and for the updating of its parameters. A comparison between numerical and experimental results is finally provided.

Influence of Noise in Computer-Vision-Based Measurements on Parameter Identification in Structural Dynamics

Nowadays, consumer electronics offer computer-vision-based (CV) measurements of dynamic displacements with some trade-offs between sampling frequency, resolution and low cost of the device. This study considers a consumer-grade smartphone camera based on complementary metal-oxide semiconductor (CMOS) technology and investigates the influence of its hardware limitations on the estimation of dynamic displacements, modal parameters and stiffness parameters of bolted connections in a laboratory structure. An algorithm that maximizes the zero-normalized cross-correlation function is employed to extract the dynamic displacements. The modal parameters are identified with the stochastic subspace identification method. The stiffness parameters are identified using a model-updating technique based on modal sensitivities. The results are compared with the corresponding data obtained with accelerometers and a laser distance sensor. The CV measurement allows lower-order vibration modes to be identified with a systematic (bias) error that is nearly proportional to the vibration frequency: from 2% for the first mode (9.4 Hz) to 10% for the third mode (71.4 Hz). However, the measurement errors introduced by the smartphone camera have a significantly lower influence on the values of the identified stiffness parameters than the numbers of modes and parameters taken into account. This is due to the bias-variance trade-off. The results show that consumer-grade electronics can be used as a low-cost and easy-to-use measurement tool if lower-order modes are required.

Two-dimensional motion estimation using phase-based image processing with Riesz transform

As a kind of photogrammetry technique, phase-based motion estimation (PME) has proven to be a powerful image/video processing algorithm in the extraction of structural dynamics, due to its full-filed resolution and no requirement of surface preparation, compared to conventional structural testing. Although images and videos employed in PME are two-dimensional arrays, PME only extracts phase information in a single direction at a time. Therefore, extracting two-directional motions at the same time is needed to avoid two times of PME implementation. To address this issue, Riesz-transform is integrated to the phase-based motion estimation algorithm, and Riesz transform PME (RPME) is proposed in this work. The concept of plane phase is extended to spatial phase using Riesz transform to process images, because Riesz transform is able to extract phase information in two directions simultaneously. Then quaternion is utilized to derive the theoretical relationship between spatial phase and structure motions. In order to obtain the mono-component image sequence required in Riesz transform, an ideal narrow bandpass filter is constructed based on the set of Butterworth low-pass filters. Due to the capability of recognizing two-directional motions simultaneously using the proposed RPME, a much-improved efficiency of structural dynamics identification is observed. In addition, Riesz transform extracts instantaneous phase, thus the motion recognition accuracy is improved as well. To validate the benefit of RPME, both numerical simulation and laboratory-scale experiments are conducted, and motions in x and y directions are extracted simultaneously, with a drastically increased accuracy in both the simulation and experimental validations.

Vibration testing and performance evaluation of Hagia Sophia bell tower after recent restoration

Historical structures are very valuable in terms of culture and history because they are the legacy of the past and the trust of the future. These structures require structural investigation and assessment to survive their life. By developing technology, the continuous and/or partial monitoring of these structures has become widespread in many parts of world for last decades. This study presents the structural dynamic parameter identification and the seismic performance evaluation of Hagia Sophia Bell Tower. This historical tower was built by using masonry cut stones in 1204 in Trabzon, Türkiye. Many restorations were made on the bell tower in different times in the past and the last one was executed in 2020. After this restoration, ambient vibration tests were performed on the tower by using developed measurement systems. The dynamic characteristics were attained by analyzing the collected data and were compared the results of previous studies to determine the effects of the last restoration. Also, an initial finite element model was generated by using solid elements in ANSYS Workbench software and the model was calibrated according to the experimental natural frequencies attained from the last restoration. The structural performance was evaluated by performing seismic analyses according to the current Türkiye Building Earthquake Code by considering the local site effects and seismicity. These analyses were performed on the weak direction of the tower in the initial and calibrated finite element models. The maximum top displacement, drift ratios, principal stress values and their distributions were determined and the seismic vulnerability was evaluated by considering these values.

Time-domain model identification of structural dynamics from spatially dense 3D vision-based measurements

A novel approach is presented for the time-domain system identification of structural dynamic components exploiting the high spatial density of vision-based measurements. By using spatially dense measurements, the number of spatial measurement points is much larger than the dimensionality of the underlying dominant dynamics (i.e., the number of measurement points needed to meet observability of the targeted dynamics). This opens up the potential to develop new experimental identification methods that use this spatial overdetermination which were out of reach with conventional discrete sensors. The new approach presented in this paper directly extracts a relatively noise-free, low-order set of dynamic states by projecting the spatially dense time-domain measurements on a low-order dominant deformation motion basis. The basis is constructed by applying an over-complete singular value decomposition on the measurements. These dynamic states together with their numerically calculated first and second order time-derivatives are then used in a two-step identification of the structural dynamic parameters. Here, the structure of the model to identify is based on a-priori physical knowledge of the underlying set of partial differential equations, unlike a purely data-driven method. This approach has the benefits of providing a mathematical formulation that is straightforward to understand and implement and is time-efficient to solve. The presented approach is experimentally validated on a clamped plate as well as on a flexibly suspended plate which requires a correction of the rigid body motion. The identified models have shown to provide an accuracy up to 1 × 10−5 m with respect to the dominant measured motion components in both validation cases.

An Innovative Structural Dynamic Identification Procedure Combining Time Domain OMA Technique and GA

In this paper an innovative and simple Operational Modal Analysis (OMA) method for structural dynamic identification is proposed. It combines the recently introduced Time Domain–Analytical Signal Method (TD–ASM) with the Genetic Algorithm (GA). Specifically, TD–ASM is firstly employed to estimate a subspace of candidate modal parameters, and then the GA is used to identify the structural parameters minimizing the fitness value returned by an appropriately introduced objective function. Notably, this method can be used to estimate structural parameters even for high damping ratios, and it also allows one to identify the Power Spectral Density (PSD) of the structural excitation. The reliability of the proposed method is proved through several numerical applications on two different Multi Degree of Freedom (MDoF) systems, also considering comparisons with other OMA methods. The results obtained in terms of modal parameters identification, Frequency Response Functions (FRFs) matrix estimation, and structural response prediction show the reliability of the proposed procedure.

Influence of the ground on the structural identification of a bell-tower by ambient vibration testing

The article revolves around the structural identification technique through dynamic in situ tests trying to unravel the contribution of Soil Structure Interaction (SSI). The issue is addressed by considering the bell tower of Santa Sofia in Benevento (Italy) as a case study. Together with the homonymous church, the monastery and the fountain, the bell tower is part of a monumental complex included in the UNESCO World Heritage List since 2011. As the tower is completely separated from the other buildings of the complex, from a structural viewpoint it is quite a simple structure but likely to be affected by SSI. The latter phenomenon in some way could dictate the tower static and dynamic response, thus affecting the overall structural dynamic identification process. Invasive investigations are not usually allowed on cultural heritage due to preservation requirements. Thus, the paper proposes a simple but effective procedure for obtaining the data set required for both structure and soil characterization through noninvasive in-situ tests. The dynamic response of the subsoil at the tower site was firstly identified by reproducing the experimental amplification function provided by geophysical tests. Later, the results of an ambient vibration test performed on the bell tower have been interpreted and used to calibrate two refined 3D finite element models of the tower, one having the structure with a restrained base and another with a base compliant with the reality found. In the latter case, a suitable portion of the soil below the tower was included in the analysis domain. The contribution of the ground has been ascertained to move towards a reliable dynamic identification of the built cultural heritage. • Procedure for structure and soil data set characterization by noninvasive in-situ tests. • The importance of SSI on the correct identification of the structure behavior. • Combined geotechnical and structural optimization procedure to validate a FE model.

Load identification with regularized total least-squares method

Load identification in structural dynamics is an ill-conditioned inverse problem, and the errors existing in both the frequency response function matrix and the acceleration response have a great influence on the accuracy of identification. The Tikhonov regularized least-squares method, which is a common approach for load identification, takes the effect of the acceleration response errors into account but neglects the effect of the errors of the frequency response function matrix. In this article, a Tikhonov regularized total least-squares method for load identification is presented. First, the total least-squares method which can minimize the errors of the frequency response function matrix and acceleration response simultaneously is introduced into load identification. Then Tikhonov regularization is used to regularize the total least-squares method to improve the ill-conditioning of the frequency response function matrix. The regularization parameter is selected by the L-curve criterion. To validate the performance of the regularized total least-squares method, a load identification simulation with two excitation loads is studied on a plate based on the finite element method and a load identification experiment with two excitation loads is conducted on an aluminum plate. Both simulation and experiment results show that the excitation loads identified by the regularized total least-squares method match the actual loads well although there are errors existing in both the frequency response function matrix and acceleration response. In experiment, the average relative error of the regularized total least-squares method is 13.00% for excitation load 1 and 20.02% for excitation load 2, whereas the average relative error of the regularized least-squares method is 35.86% and 53.09% for excitation load 1 and excitation load 2, respectively. This result reveals that the regularized total least-squares method is more effective than the regularized least-squares method for load identification.

Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force

Testing nonlinear structures to characterise their internal nonlinear forces is challenging. Often nonlinear structures are excited by harmonic forces and yield a multi-harmonic response. In many systems, particularly ones with strong nonlinearities, the effect of higher harmonics in the force and responses cannot be ignored. Even if the intended excitation is a single frequency sinusoidal force, the interaction of the shaker and the nonlinear structure can lead to harmonics in the applied force. The effects of these higher harmonics of the input force on nonlinear model identification in structural dynamics are often neglected. The objective of this study is to introduce an identification method, motivated by the alternating frequency/time approach using harmonic balance (AFTHB), which is able to consider both multi-harmonic forces and multi-harmonic responses of the system. The proposed AFTHB method can include all significant harmonics by selecting an appropriate time step and sampling frequency to guarantee the accuracy of the results. An analytical harmonic-balance-based (AHB) approach is also considered for comparison. However, the inclusion of all significant harmonics of the response in the analytical expansion of the nonlinear functions is often cumbersome. Furthermore, the AFTHB method can easily cope with complex nonlinearities such as Coulomb friction and with multi-degree of freedom nonlinear systems. Including the effect of higher harmonics in the identification process reduces the approximation error due to truncation and very accurate approximation of the balanced equations of each harmonic is obtained. The proposed identification method requires prior knowledge or an appropriate estimation of the type of system nonlinearities. However, the method of model selection may be used for a set of candidate models, and avoiding a dictionary of arbitrary candidate basis functions significantly reduces the computational costs. This paper highlights the important features of the AFTHB method to ensure accurate estimation using four simulated and two experimental examples. The effects of the number of harmonics considered, the modelling error, measurement noise and the frequency range on the quality of the estimated model are demonstrated.

Equation discovery for nonlinear dynamical systems: A Bayesian viewpoint

This paper presents a new Bayesian approach to equation discovery – combined structure detection and parameter estimation – for system identification (SI) in nonlinear structural dynamics. The structure detection is accomplished via a sparsity-inducing prior within a Relevance Vector Machine (RVM) framework; the prior ensures that terms making no contribution to the model are driven to zero coefficient values. Motivated by the idea of compressive sensing (CS) and recent results from the machine learning community on sparse linear regression, the paper adopts the use of an over-complete dictionary to represent a large number of candidate terms for the equation describing the system. Unlike other sparse learners, like the Lasso and its derivatives, which are potentially sensitive to hyperparameter selection, the proposed method exploits the principled means of fixing priors and hyperpriors that are available via a hierarchical Bayesian approach. The approach is successfully demonstrated and validated via a number of simulated case studies of common Single-Degree-of-Freedom (SDOF) nonlinear dynamic systems, and on two challenging experimental data sets.

A Critical Review of Nonlinear Damping Identification in Structural Dynamics: Methods, Applications, and Challenges.

In recent decades, nonlinear damping identification (NDI) in structural dynamics has attracted wide research interests and intensive studies. Different NDI strategies, from conventional to more advanced, have been developed for a variety of structural types. With apparent advantages over classical linear methods, these strategies are able to quantify the nonlinear damping characteristics, providing powerful tools for the analysis and design of complex engineering structures. Since the current trend in many applications tends to more advanced and sophisticated applications, it is of great necessity to work on developing these methods to keep pace with this progress. Moreover, NDI can provide an effective and promising tool for structural damage detection purposes, where the changes in the dynamic features of structures can be correlated with damage levels. This review paper provides an overview of NDI methods by explaining the fundamental challenges and potentials of these methods based on the available literature. Furthermore, this research offers a comprehensive survey of different applications and future research trends of NDI. For potential development and application work for nonlinear damping methods, the anticipated results and recommendations of the current paper can assist researchers and developers worldwide to find out the gaps and unsolved issues in the field of NDI.

Structural Dynamic Load and Parameter Identification Based on Dummy Measurements of Displacement

Structural load and parameter identification are the essential contents in the field of structural dynamics, and some studies pay attention to the coupled recognition of uncertain structure parameters as well as unacquainted loads. Gillijns and De Moor presented the Kalman-type filter, which was used in the work for coupled identification as the unabbreviated form of GDF. However, it has been demonstrated that it is unstable for the extended GDF (EGDF) method, drifting in the identified unacquainted loads as well as displacement, just like most previous identification methods based on the least-square algorithm. In order to deal with this unstable issue, this paper applied the dummy measurements of displacements on a position level and modifies the EGDF algorithm using the information integration method about the accelerated measurements with dummy measurements. Numerical example of a truss is used for validating the applicability of the method in the work, and an influence of covariance matrices in dummy displacements is also considered.

Sparse and Random Sampling Techniques for High-Resolution, Full-Field, BSS-Based Structural Dynamics Identification from Video.

Video-based techniques for identification of structural dynamics have the advantage that they are very inexpensive to deploy compared to conventional accelerometer or strain gauge techniques. When structural dynamics from video is accomplished using full-field, high-resolution analysis techniques utilizing algorithms on the pixel time series such as principal components analysis and solutions to blind source separation the added benefit of high-resolution, full-field modal identification is achieved. An important property of video of vibrating structures is that it is particularly sparse. Typically video of vibrating structures has a dimensionality consisting of many thousands or even millions of pixels and hundreds to thousands of frames. However the motion of the vibrating structure can be described using only a few mode shapes and their associated time series. As a result, emerging techniques for sparse and random sampling such as compressive sensing should be applicable to performing modal identification on video. This work presents how full-field, high-resolution, structural dynamics identification frameworks can be coupled with compressive sampling. The techniques described in this work are demonstrated to be able to recover mode shapes from experimental video of vibrating structures when 70% to 90% of the frames from a video captured in the conventional manner are removed.

Neural network supported inverse parameter identification for stability predictions in milling

A new approach for the inverse identification of structural dynamics and process parameters in milling operations is presented. An algorithm is fed with process information and the stability state of recorded cuts. By comparing stability model predictions with experimental data, the underlying relationships and governing parameters are estimated with the help of Artificial Neural Networks. The capabilities of the approach are demonstrated using a simulative example and two experimental studies. The algorithm shows to be capable of approximating unknown relationships such as spindle speed dependent dynamics, which in turn allows for accurate stability predictions without the need for extensive dedicated measurements.