Eigensystem Realization Algorithm Research Articles

Reconstructing rodent brain signals during euthanasia with eigensystem realization algorithm (ERA)

We accurately reconstruct the Local Field Potential time series obtained from anesthetized and awake rats, both before and during CO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} euthanasia. We apply the Eigensystem Realization Algorithm to identify an underlying linear dynamical system capable of generating the observed data. Time series exhibiting more intricate dynamics typically lead to systems of higher dimensions, offering a means to assess the complexity of the brain throughout various phases of the experiment. Our results indicate that anesthetized brains possess complexity levels similar to awake brains before CO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} administration. This resemblance undergoes significant changes following euthanization, as signals from the awake brain display a more resilient complexity profile, implying a state of heightened neuronal activity or a last fight response during the euthanasia process. In contrast, anesthetized brains seem to enter a more subdued state early on. Our data-driven techniques can likely be applied to a broader range of electrophysiological recording modalities.

A mechanics-informed neural network method for structural modal identification

Modal identification is one of the core topics within the realm of structural health monitoring (SHM). In this study, we summarize four modal mechanical properties and propose a mechanics-informed neural network (MINN) method for structural modal identification. The proposed MINN method incorporates the sparsity of the data in the time–frequency domain and cross-correlation minimization in the time domain into the neural network to obtain modal parameters, which uses sparsity constraint and cross-correlation minimization constraint to obtain the accurate modal responses and mode shapes. Subsequently, modal frequencies and damping ratios can be derived from the modal responses. The proposed MINN method is verified by numerical simulations and two actual suspension bridges. Compared with traditional methods, the proposed MINN method has two major advantages. Firstly, the proposed MINN method presents explicit mathematical equations to distinguish the modes and the spurious modes, which obviates the necessity for priori information such as model order or time-consuming manual intervention to distinguish the modes and the spurious modes. Therefore, it can be implemented adaptively to determine the modal order and obtain the modal parameters. Secondly, the proposed MINN method can obtain a greater number of accurate modal parameters than traditional methods and achieves an increase of 102.6%, 43.4%, and 31.5% in the number of accurate results when compared to covariance-driven stochastic subspace identification (SSI-COV), data-driven stochastic subspace identification (SSI-DATA) and the natural excitation technique and the eigensystem realization algorithm (NExT-ERA), respectively. Therefore, the proposed MINN method provides an adaptively modal identification method that has clear modal mechanical properties to distinguish the modes and the spurious modes and can obtain a greater number of accurate results.

The Determination of Effective Modes of Wind-Bridge Coupling System Based on Stabilization Clustering Method

Modal identification is the core content of the full-bridge aeroelastic model wind tunnel test. Modal consistency is the most direct and effective basis to ensure that the model and the real bridge meet the similarity criteria. Accurate, simple and fast identification of modal parameters has very important practical significance for the evaluation and correction of aeroelastic models. In this paper, the eigensystem realization algorithm (ERA) and stochastic subspace identification (SSI) is improved, and the automatic identification theory of effective modes of bridge aeroelastic model based on stable clustering method is proposed. The stable diagram eliminates the unstable modes by comparing the results of different system orders, and the pedigree clustering further polarizes the stable modes to obtain multi-order and high-precision system modes. Numerical simulation examples and wind tunnel engineering examples show that the method has high accuracy and good adaptability, and can solve the problem of unstable damping identification results to a certain extent. In the wind tunnel test, the stable clustering method is one of the effective methods to identify the modal of the bridge aeroelastic model excited by the wind environment.

FEM-based eigenstructure recovery of a space truss with active members

Abstract Large truss structures have many potential applications in space, such as antennas, telescopes and space solar power plants. In this scenario, a natural concern is the susceptibility of these lightweight structures to be damaged during their operational life, due to impacts, transient thermal states and fatigue phenomena. The inclusion of active elements, equipped with sensor/actuator systems capable of modulating their shape and strength, makes it possible to transform the truss into a smart structure capable of remedying the damage, once it is detected. In this paper, a procedure is described that is capable of restoring at least the basic functionality of a composite truss for space applications, starting with the observation that damage has occurred, regardless of its specific location. The system eigenstructure is used as a benchmark for damage detection, as well as a target characteristic for the subsequent restoration activity. The observer/Kalman filter identification algorithm (OKID), in cascade with the eigensystem realization algorithm (ERA), is adopted to reconstruct, from sensor recordings, the dynamic response of the truss in terms of system state-space representation and eigen-characteristics. Finally, a static output feedback control is developed to recover the low-frequency dynamic behaviour of the truss. The entire procedure is tested using finite element analysis. All activities are coordinated in an innovative procedure that, within a unique Python language code, automatically generates finite element (FE) models, launches finite element analysis (FEA), extracts output data, implements OKID-ERA, processes the control law and applies it to the final FE simulation.

Identification of flutter boundary of a bridge deck section using CFD and flutter margin analysis

Aeroelastic flutter identification of a two-dimensional bridge deck section using time domain techniques is studied. Aeroelastic simulations are performed using the aeroelastic solver available in open source OpenFOAM 5.0, wherein aerodynamic loads are computed using Unsteady Reynolds Average Naiver–Stokes (URANS) solver. The bridge deck section, modelled as a rigid body, exhibits pitch and heave degrees of freedom. Time domain system identification techniques, which include VAR and ERA (Vector auto-regressive and Eigensystem realization algorithm), are used to extract frequency and damping parameters from the aeroelastic response for various wind speeds.Two approaches are used for identification of the flutter boundary. The first consists of tracking the behaviour of damping and identifying the speed at which damping vanishes. The second approach is based on the flutter margin for discrete-time system (FMDS), which exhibits a linear behaviour with dynamic pressure in the vicinity of flutter.Results presented indicate that the ERA yielded slightly better estimates of damping compared to VAR. Furthermore, the FMDS parameter provided a reasonable estimate of the flutter boundary using only two data points, suggesting that this is an efficient strategy (as compared to tracking the damping) for flutter identification when the cost per aeroelastic response data point is high.

Modal identification with uncertainty quantification of large‐scale civil structures via a hybrid operation modal analysis framework

SummaryIn operational modal analysis (OMA), only structural responses are typically available. In this context, bias and variance (uncertainty) errors may exist in modal estimates (especially damping estimates), resulting in inaccurate determination of the modal properties of large‐scale structures under harsh excitations. To this end, a hybrid OMA framework based on the modal decoupling, the natural excitation technique, the random decrement technique (RDT), and improved eigensystem realization algorithm (ERA) with the automated stabilization diagram is presented to perform high‐accuracy modal estimates with uncertainty quantification for large‐scale structures under normal and severe ambient excitations. The accuracy and effectiveness of the hybrid framework for identifying the modal parameters are validated by numerical simulation study of a framework structural model. Furthermore, the hybrid framework is applied to analyze recorded acceleration responses of a supertall building with 600‐m height under normal excitations and typhoon condition to verify its applicability in field measurements. The numerical simulation and field measurement studies demonstrate that the hybrid framework can not only perform precise modal estimations with uncertainty quantification through a single ambient vibration measurement but also effectively reveal the variations of modal properties of supertall structures under harsh excitations from multiple perspectives. This paper aims to enhance the reliability and accuracy of modal estimation for engineering structures and further provide insight into the variations of dynamic properties of large‐scale civil structures under severe excitations.

The new Subspace-based poly-reference Complex Frequency (S-pCF) for robust frequency-domain modal parameter estimation

Subspace identification has been widely used in modal parameter estimation. The formulation of a parametric subspace-driven modal identification technique is achieved by using the Singular Value Decomposition (SVD) to remove most the uncertainties present in the null space of the system matrices used in the identification process, which leads to a more robust estimation of the modal properties. This idea has been used in the formulation of time domain modal identification techniques like the (time-domain) Eigensystem Realization Algorithm and the Stochastic Subspace identification techniques. In this paper, a subspace implementation of the new poly-reference Complex Frequency (pCF) formulated in Modal Model is proposed. The idea is to combine SVD with the new pCF to derive a new system identification technique that operates in the frequency domain by using either the Frequency Response Function or the Half Spectrum as primary data. Similarly to the ERA, the idea behind the subspace implementation of the pCF is to use different subspaces of the observability and frequency-domain controllability matrices, and carry out eigen-system realizations to estimate the modal properties corresponding to each chosen subspace. In order to illustrate its robustness, the subspace-driven pCF is applied to a simulated and two practical application examples.

Data-Driven Balanced Truncation for Predictive Model Order Reduction of Aeroacoustic Response

Rapid prediction of the aeroacoustic response is a key component in the design of aircraft and turbomachinery. In this work, we propose a technique for highly accelerated prediction of aeroacoustic response using a data-driven model reduction approach based on the eigensystem realization algorithm (ERA). Specifically, we create and compare ERA reduced-order models (ROMs) based on the training data generated by solving the linearized and nonlinear Euler equations, and we use them to predict the aeroacoustic response of an airfoil in a purely predictive setting subject to different types of gust loading. Activating each input channel separately in the full-order model (FOM) to generate the Markov sequence for training makes it computationally challenging to use the ERA in aeroacoustics applications. We address this bottleneck by first proposing a multifidelity gappy POD method to reduce the computation cost on the FOM and ROM levels by querying the high-resolution FOM only for the input channels identified by gappy POD. Second, we use tangential interpolation at the ROM level to reduce the size of the Hankel matrix. The proposed methods enable application of the ERA for accurate online acoustic response prediction, and they reduce the offline computation cost of ROMs.

Experimental modal analysis of a single-link flexible robotic manipulator with curved geometry using applied system identification methods

In this paper, the principal time-domain system identification methods are studied and used to carry out the experimental modal analysis of a single-link flexible manipulator with curved geometry in a comparative fashion. The identification process carried out in this study is aimed at deriving first-order state-space dynamical models and second-order configuration-space dynamical models of the single-link flexible manipulator by using an array of fundamental system identification procedures, which includes the ARX (AutoRegressive eXogenous method), SSEST (State-Space ESTimation method), N4SID (Numerical Algorithm for Subspace State-Space System Identification), ERA/OKID (Eigensystem Realization Algorithm combined with the Observer/Kalman Filter Identification method), and TFEST (Transfer Function ESTimation method) methods. The main goal of this paper is, therefore, to perform a comparative study between the most fundamental system identification procedures applied to the numerical and experimental analysis of the structural vibrations of a flexible manipulator having a curved geometric shape. First, this paper poses the theoretical foundations for the development of the numerical study and the experimental testing to be performed for the case study. Subsequently, the flexible manipulator analyzed in this work is modeled with various levels of complexity, which range from a simple lumped parameter model to a linear finite element model developed by integrating the interconnections between the SOLIDWORKS and ANSYS software. By doing so, the computational procedures applied to the time-domain experimental measurements of the dynamic behavior of the flexible manipulator allow for reconstructing first-order and second-order mechanical models of the structural system of interest in the MATLAB simulation environment. The numerical results and the experimental tests reported in this investigation demonstrate the effectiveness of all the time-domain system identification approaches considered in the paper.

A Novel Method for Seismic Resilience Assessment of Urban Hospital Network Systems Based on a Real-Time Simulation Model

Earthquake hazards may cause a significant loss to urban hospital network system (UHNS), including hospitals and medical transportation networks. As such, systematic seismic resilience assessment of such systems is of paramount importance to reduce loss and optimize casualty care during earthquakes. For that purpose, this paper proposes a novel method for assessing the seismic resilience of UHNS that considers the logical dependencies or coupling among the system’s components, such as the casualty sources, the hospitals and the medical transportation networks. A resilience index is defined as the ratio between the average “shortest” time for a casualty to receive medical treatment before and after an earthquake. The time consists of both transportation time to a hospital and queuing time at the hospital. To obtain the shortest time, a real-time simulation model is proposed that considers the casualty sources, the changes in road traffic, the updates of Origin-Destination (OD) matrix for transportation time, the modifications of waiting time in hospital, the path reselection by casualty, and the changes in functionalities of bridges, hospitals and roads. The functionalities are obtained by analyzing fragility models, calculating residual functionality and estimating functionality recovery times. To calculate the fragilities of bridges and hospitals, a refined nonlinear finite element (FE) analysis is performed based on a general FE software, OpenSees, and the damages are obtained for various structural and nonstructural components, e.g. column, stairs and CT scanner of hospitals, as well as piers, bearings and abutments of bridges. The proposed method is demonstrated in a seismic resilience assessment of a realistic UHNS in Xiamen city of China and provides valuable references to assessments of seismic resilience of UHNS.

An Eigensystem Realization Algorithm for Identification of Modal Parameters of Nonviscous Damping Structure System

In this paper, a modified eigensystem realization algorithm for modal parameter identification and relaxation parameter is extended from a viscous damping system to a nonviscous damping system. The equation of motion with nonviscous damping in second-order form is expressed in the state space formulation. The eigenvalues of the second-order form equation are proved equal to the state space formulation. The extended method is based on the proposed nonlinear relationship between the eigenvalues and the damping parameters of a nonviscous damping system. The identified procedure of the proposed method is given in detail. Finally, the method is validated using three numerical examples for assessing its accuracy.

Automatic modal identification via eigensystem realization algorithm with improved stabilization diagram technique

Efficient and automatic identification of modal parameters becomes increasingly important for real-time structural health monitoring (SHM) of civil structures. As spurious modes usually exist as a key problem for most output-based identification methods, great efforts have been made to eliminate them typically via stabilization-diagram techniques. However, the quality of traditional stabilization diagrams depends on preset parameters whose values usually vary from one case to another, which makes the method to be less objective and low efficient. This article proposes an improved stabilization-diagram technique, through combined usage of Monte-Carlo sampling simulation, as well as fuzzy C-means (FCM) clustering and three-stage sifting manipulations. While the Monte-Carlo simulation aims to generate more robust stable-axis, the sifting and clustering manipulations can further remove outliers and discriminate true modal results. The improved stabilization-diagram technique is then applied to two mainstream modal identification methods, i.e., eigensystem realization algorithm (ERA) and stochastic subspace identification (SSI) under the context of both a simulation study on a dynamic system and a field research about a super-tall building. Results through comparison demonstrate that the improved stabilization-diagram technique can facilitate ERA and SSI to identify modal parameters automatically and effectively at a comparably good accuracy. However, ERA outperforms SSI evidently in terms of computational efficiency (upmost 15 times faster), which is attractive for real-time SHM. Parametric analysis has been also conducted to examine detailed performance of ERA aided by the proposed stabilization-diagram technique. Overall, the aforementioned method can be adopted to achieve a good balance between identification effectiveness and computational efficiency in an automatic working pattern, and has application prospect for real-time SHM of civil structures.

In-Network Processing or Feature Compressive Sensing? Case Study of Structural Health Monitoring With Wireless Sensor Networks

In many domain-specific monitoring applications of wireless sensor networks (WSNs), such as structural health monitoring (SHM), volcano tomography, and machine diagnosis, all the raw data in WSNs are required to be gathered to the sink where a specialized centralized algorithm is then executed to extract some global features or model parameters. To reduce the large-scale raw data transmission while guaranteeing the global feature quality, there are two kinds of solutions: one is in-network processing, which generally needs to distribute the centralized computation of feature extraction into networks. Another solution is compressive sensing (CS) followed with the feature extraction (called feature CS in this article). An interesting question is: for in-network processing and feature CS, which kind of solutions is more cost efficient to accomplish the task of feature extraction? This question is seldom studied. To answer it, we take the case of SHM with WSNs along with the classic feature extraction algorithm, i.e., the Eigen-system realization algorithm (ERA), and appropriately design two novel routes for in-network processing and feature CS, respectively. Both theoretical analysis of the two solutions’transmission cost and numerous simulations have been conducted. Based on the comparison results, we summarize some guidelines on the solution choice for different kinds of WSNs for SHM. In addition, we find that, instead of guaranteeing the quality of raw data reconstructed, CS with guaranteeing the quality of feature extracted is usually more meaningful and cost efficient.

Triggering of galloping in structures at low Reynolds numbers

The fundamental mechanisms that are important for the triggering of galloping in a flow-induced vibration (FIV) system consisting of the flow past an elastically-mounted body (D-section, isosceles-triangular, rectangular) is investigated in this paper using three key-enabling methodologies: namely, high-fidelity full-order model/computational fluid dynamics simulations, modal analysis based on the determination of an data-driven model using the eigensystem realization algorithm, and use of the Den Hartog stability (galloping) criterion for the assessment of the aerodynamically unstable behavior of the system obtained from classical quasi-steady theory. The synthesis of the results from the application of these three key-enabling technologies is used to study the effect of the Reynolds number Re, the mass ratio m∗, the cross-sectional geometry and the angle of attack of the incident wind direction relative to the orientation of the elastically-mounted body on the suppression or initiation of galloping. In the application of data-driven modal analysis to a FIV system with coupled modes, the importance of identifying correctly which of the coupled modes correspond to the structure mode (SM) possibly taking into account mode switching is stressed, and the failure to do so is shown to lead to a significant underestimation of the value of the reduced velocity Ur associated with the onset of galloping. The range of values of Ur where the SM is positive is related to the flutter lock-in regime for smaller values of Ur (typically for Ur≤7) and to the galloping regime for the larger values of Ur (typically for Ur≥10). The application of data-driven modal analysis to a FIV system shows that increasing Re and decreasing m∗ has two effects: namely, enhancement of the coupling between the structure and wake modes and increases of the range of Ur values where the SM exhibits a positive growth rate. Data-driven modal analysis and the Den Hartog stability criterion is applied to explain the recently observed phenomenon of the collapse of galloping for a rectangular cylinder when the side ratio is decreased below a critical threshold value (between about 0.1 and 0.2). It is shown that galloping appears and disappears when the flat face of a body in directed into (windward of) or away from (leeward of) the incident wind direction. An investigation of the effects of the cross-sectional geometry of the body on the triggering of soft- or hard-galloping is undertaken.

Non-Contact Measurement and Identification Method of Large Flexible Space Structures in Low Characteristic Scenes.

The end-operation accuracy of the satellite-borne robotic arm is closely related to the satellite attitude control accuracy, and the influence of the vibration of the satellite's flexural structure on the satellite attitude control is not negligible. Therefore, a stable and reliable vibration frequency identification method of the satellite flexural structure is needed. Different from the traditional non-contact measurement and identification methods of large flexible space structures based on marker points or edge corner points, the condition of non-marker points relying on texture features can identify more feature points, but there are problems such as low recognition and poor matching of features. Given this, the concept of 'the comprehensive matching parameter' of scenes is proposed to describe the scene characteristics of non-contact optical measurement from the two dimensions of recognition and matching. The basic connotation and evaluation index of the concept are also given in the paper. Guided by this theory, the recognition accuracy and matching uniqueness of features can be improved by means of equivalent spatial transformation and novel relative position relationship descriptor. The above problems in non-contact measurement technology can be solved only through algorithm improvement without adding hardware devices. On this basis, the Eigensystem Realization Algorithm (ERA) method is used to obtain the modal parameters of the large flexible space structure. Finally, the effectiveness and superiority of the proposed method are verified by mathematical simulation and ground testing.

Statistical characteristics of modal damping of long-span suspension bridge at different wind speeds

The present paper combined the natural environment excitation technology (NExT) with the eigen system realization algorithm (ERA) to identify the modal parameters of a suspension bridge. Firstly, the critical parameters in NExt–ERA, such as record length, window length, and ranks of the Hankel matrix, and their influence on identification accuracy have been discussed. Subsequently, based on the acceleration series obtained from the Xihoumen Bridge Health Monitoring System, 3015 sets of modal frequencies and modal damping ratios of the Xihoumen Bridge were identified under 7 sets of wind speeds by the NExt–ERA. Finally, the probability distribution and confidence interval of the structural modal damping ratios were analyzed. Besides, the dependence of identified frequencies damping ratios on wind speed was also discussed. The results show that at the same wind speed, the mean value, and variance of the torsional and lateral mode damping ratios are larger than those of the vertical mode, but this difference gradually decreases with the increment of wind speed. The modal damping ratios along three directions under different wind speeds all follow the generalized extreme value distribution, but wind speed affects the tailing properties of probability distribution of the vertical and torsional mode damping ratios. The estimated damping ratios could provide references for structural design and vibration control of similar long-span bridges.

Data-driven stability analysis via the superposition of reduced-order models for the flutter of circular cylinder submerged in three-dimensional spanwise shear inflow at subcritical Reynolds number

In this paper, we present a novel data-driven theory for the stability analysis of a flow-induced vibration (FIV) system consisting of an elastically mounted circular cylinder submerged in three-dimensional (3D) spanwise shear inflow at a subcritical Reynolds number. The presented data-driven theory separates the cylinder into several elements along the spanwise direction and treats the aerodynamics of each element as a two-dimensional (2D) situation subject to a uniform inflow. An eigensystem realization algorithm is constructed to obtain the separate 2D flow reduced-order model (ROM) for each element, and then, the superposition of those 2D ROMs (SROM) is processed to obtain the simplified 3D flow ROM. The simplified 3D flow ROM is coupled with the structural model to perform a linear stability analysis of the FIV system under study. The proposed data-driven technique demonstrates high consistency with the high-fidelity full-order model (FOM) with regard to the prediction of flutter lock-in boundaries while being more time-efficient, whereas the traditional direct 3D data-driven analysis involves significant errors. The growth rate obtained using SROM is negatively correlated with the lagging time (reflected in the FOM calculation) for the FIV system to evolve from the initial stationary state to the final equilibrium state. The evolution of the structural instability range with the variation in the mass ratio is analyzed/predicted by the proposed data-driven theory. The determination of the lock-in regime using the FOM is accompanied by a careful discussion of the associated dynamical responses, including phase differences, structural oscillation frequencies, lift coefficients, and wake patterns.

Enhanced nonlinear state–space identification for efficient transonic aeroelastic predictions

Transonic aerodynamic systems exhibit strong nonlinearities due to various factors such as flow separations and shock wave oscillations. Thus, transonic aerodynamic modeling methods based on system identifications have attracted increasing attention. However, the dimensions of the models constructed via the current system identification methods are so high that it is difficult to predict transonic flutters and limit cycle oscillations simultaneously. This paper proposes an enhanced nonlinear state–space modeling method to identify a two-dimensional aerodynamic system in the transonic region. At first, the parsimonious linear model with modified inputs is identified by using the eigensystem realization algorithm. The model order is reduced by substituting the generalized displacement of the first-order mode (dominated by plunge) with its generalized velocity in the inputs. The polynomial functions are then used to represent the nonlinearities in the transonic aerodynamic systems. The polynomial functions do not contribute to the system linearization around the equilibrium such that the linear and nonlinear modeling stages are independent. The coefficients of these nonlinear terms are determined via nonlinear optimization. Finally, a nonlinear aerodynamic model is established and applied to aeroelastic applications. To demonstrate the accuracy and efficiency of this method, a two-dimensional, transonic aeroelastic wing with an NACA0012 profile is investigated. The simulation results show that the nonlinear state–space model with modified inputs improves the efficiency and accuracy of transonic aerodynamic nonlinear modeling. Moreover, the aerodynamic model coupled with the structural model can accurately predict the transonic flutter boundary and limit cycle oscillations.

Deep learning for predicting frequency lock-in of a freely vibrating sphere

In this paper, we present a deep learning-based reduced-order model (DL-ROM) for the stability prediction of unsteady three-dimensional fluid–structure interaction systems. The proposed DL-ROM has the format of a nonlinear state-space model and employs a recurrent neural network with long short-term memory (LSTM) cells. We consider a canonical fluid–structure system of an elastically mounted sphere coupled with the incompressible fluid flow in a state-space format. Specifically, we develop a nonlinear data-driven coupling for predicting the unsteady forces and the vortex-induced vibration (VIV) lock-in of the freely vibrating sphere in a transverse direction. We design an input–output relationship as a temporal sequence of force and displacement datasets for a low-dimensional approximation of the fluid–structure system. Based on the prior knowledge of the VIV lock-in process, the input function contains a range of frequencies and amplitudes, which significantly affects the system realization ability and enables an efficient DL-ROM without the need for a massive training dataset for the low-dimensional modeling. Once trained, the network provides a nonlinear mapping of input–output dynamics that can predict the coupled fluid–structure dynamics for a longer horizon via the feedback process. By integrating the LSTM network with the eigensystem realization algorithm (ERA), we construct a data-driven state-space model for the reduced-order stability analysis. We investigate the underlying mechanism and stability characteristics of VIV of a freely vibrating sphere via an eigenvalue selection process. Using the reduced-order eigenvalue analysis, we characterize the vibrating sphere-wake lock-in phenomenon and demonstrate that the lock-in responds at preferred vibration frequencies. To understand the frequency lock-in mechanism, we study the eigenvalue trajectories for a range of the reduced oscillation frequencies and the mass ratios. Consistent with the full-order simulations, the frequency lock-in branches are accurately captured by the combined LSTM-ERA procedure. The proposed DL-ROM aligns with the development of physics-based digital twin of engineering systems involving moving boundaries and fluid–structure interactions.

An improved NExT method for modal identification with tests validation

The Natural Excitation Technique (NExT) is widely used in structural modal parameter identification. However, the cross-correlation function is susceptible to the mode shape of each order, which is obtained by the traditional NExT method combined with other modal identification methods between the two measuring points, resulting in large errors of the identified frequency and damping ratio of various modes. Therefore, in this study, to obtain the modal responses of the target order correctly and eliminate interaction of various modes, a new combined NExT method with improved Empirical Mode Decomposition (EMD) method is developed. The improved NExT method is introduced firstly, then, the structural modal parameters are identified by five different methods, which are Ibrahim Time Domain Technique, Sparse Time Domain Algorithm, Autoregressive Moving Average timing method, Least Square Complex Exponential and Eigensystem Realization Algorithm respectively. The correction and improvement of the new method are verified through a simple-supported beam experiment and a shaking table test of a 12-story benchmark tall building at Tongji University. The structural modal parameters are identified and compared through adopting traditional NExT method and the proposed new NExT algorithm. Results illustrate that the improved NExT algorithm in this paper has a higher accuracy and effectiveness than the traditional one in structural modal parameter identification.