Variation Of Modal Parameters Research Articles

Self-sensing sliding mode control of workpiece chatter based on accurate prediction of machining vibration

The previous works concerning active chatter suppression in milling systems are generally carried out based on specially designed tool holders or spindles. Due to the continuous removal of materials, however, the workpiece system cannot be treated as quasi-static or rigid. In this paper, a manufacturing system based on the digital twins (DT) model and sliding mode (SM) controller is developed to suppress the milling chatter of thin-walled workpieces. A single degree of freedom (DOF) model of the workpiece is adopted to describe the milling system. The developed SM algorithm exhibits a good performance under the variations of modal parameters, cutting parameters, unmodeled dynamics, etc. To provide accurate control feedback, a DT model of workpiece vibration is established by presenting a self-sensing predictive method. The predictive methods are implemented based on the cooperation of the combination methods of beam functions (CMOBF) and the mode superposition method (MSM). In addition, the predictive accuracy is discussed quantitatively by establishing a dataset of error coefficients. The data of error coefficients are trained by the support vector machine (SVM) model, which is introduced to the predictive methods for further error modification. Finally, a DT framework is introduced briefly to combine the machining system and the control process. Based on the developed DT-driven manufacturing system, the information interaction between the control process and the vibrating system can be realized.

Influence of different position modal parameters on milling chatter stability of orthopedic surgery robots

This research is dedicated to exploring the dynamics of milling chatter stability in orthopedic surgery robots, focusing on the impact of position modal parameters on chatter stability. Initially, we develop a dynamic milling force model for the robotic milling process that integrates both modal coupling and regenerative effects. We then employ the zero-order frequency domain method to derive a chatter stability domain model, visually represented through stability lobe diagrams (SLDs). Through conducting hammer test experiments, we ascertain the robot's modal parameters at varying positions, enabling the precise generation of SLDs. This study also includes experimental validation of the chatter SLD analysis method, laying the groundwork for further examination of chatter stability across different positional modal parameters. Finally, our analysis of the variations in modal parameters on the stability of robot milling chatter yields a theoretical framework for optimizing cutting parameters and developing control strategies within the context of orthopedic surgery robots.

Dynamic Response Analysis of the Floor Structure under Random Crowd Excitation

The popularity of new structural systems and prestressing technology has led to the widespread use of the large-space floor structures in large buildings such as high-speed rail terminals, conference centers, and sports stadiums. The reduction of nonessential load-bearing elements and the increase in span of the structure result in a reduction in the natural frequency and damping ratio of the floor structure, while the floor is a crowded area with disorderly flow between people, which may lead to human-induced vibration problems. In order to assess the dynamic performance of the large-span floor structure under crowd load, the random crowd-floor vertical interaction equation is derived, and the correctness of the equation is verified by comparing it with the test. For the stochastic nature of walking crowds, a formulation modeling method for random crowd is proposed, including pedestrian-dynamics parameters, formulation model, and response parameters. The model is characterized by considering inter- and intrasubject variability and reflects the vertical interaction between pedestrians and the floor system. According to the random crowd-floor dynamic equation, the variation of modal parameters and acceleration response of the floor during random crowd walking are also analyzed. The research in this paper will help in analyzing the comfort of large-span floor structures under pedestrian excitation and better meet the needs of the development of lightweight large-span structures.

Uncertainty laws of experimental modal analysis with known broadband input

‘Uncertainty law’ aims at closed-form asymptotic formulas for the relationship between the identification uncertainties of modal properties (e.g., natural frequency, damping ratio) and test configuration (e.g., noise level, number and location of sensors, data duration). Existing developments focused on the case of unknown-input (ambient), where it has been found that identification uncertainty does not vanish even for noiseless instruments, essentially because the input is unknown. A natural question is then on how the uncertainty depends on test configuration when the input is known, not to mention how the configuration should be quantified. Motivated by these and related questions, this paper develops the uncertainty laws of modal parameters for well-separated modes with known single broadband input, e.g., vibration test with a single shaker as in experimental modal analysis. Asymptotic expressions for the posterior coefficient of variation of modal parameters are derived via the Fisher Information Matrix for long data and small damping scenarios. Assumptions and theory are validated using synthetic and field test data. Governing factors motivated by the theory are investigated, including the equivalent modal signal-to-noise ratio (for known input), the number of measured degrees of freedom, shaker location, and data duration. By virtue of the Cramér-Rao bound in classical statistics, the developed uncertainty laws represent the lower bound of identification uncertainty with known broadband input that can be achieved by any unbiased estimator. They provide a scientific basis for planning and managing identification uncertainties in vibration tests with known input.

Vision-based modal analysis of built environment structures with multiple drones

Unmanned Aerial Vehicles are employed for vision-based modal analysis of civil infrastructure, as they overcome range limitations of fixed cameras and measure the oscillations of a structure up close. Nevertheless, their potential is not fully exploited: they are often piloted manually and one at a time, though one drone is unable to capture high resolution displacement of a whole structure. An approach is explored here, employing multiple drones simultaneously to estimate natural frequencies and modal shapes of a structure, by synchronizing their measurement. The ability of the method to detect modal parameter variations is assessed, such that it can identify anomalies in the structure. Procedures are applied to a test structure, yielding maximum natural frequency estimation errors of 0.2% with respect to accelerometers. The results suggest the accuracy of the approach is high enough to warrant further development and support autonomous, multi-drone applications to the inspection of the built environment.

Performance Assessment of a High-Speed Railway Bridge through Operational Modal Analysis

Modal parameters are widely recognized as valuable indicators for evaluating the performance of railway bridges in structural health monitoring. A major challenge in the mode-based performance assessment is to obtain modal parameters reliably because operational factors may cause significant identification errors or reduce modal identifiability. To reduce the operational effects on mode-based assessment, vibration responses are divided according to excitation types, and then two subspace identification techniques are developed for identifying modal parameters of the railway bridge. If the bridge is only acted on by the ambient excitation, the stochastic subspace identification (SSI) is taken in this paper. If the bridge is mainly acted on by the train excitation, modal parameters are difficult to identify due to the regularly spaced and highly energetic axle loads. In this case, a deterministic stochastic subspace identification (DSSI) method is developed for improving the modal identifiability of the railway bridge under train action. The monitoring responses of a high-speed railway bridge are analyzed in this paper to track long-term modal parameters. Besides, variations of modal parameters that are related to environmental factors, operational conditions, modal orders, vibration directions, and member types are extensively compared. The results show that modal parameters can be well-identified even though the nonwhite noise excitation exists, and the performance assessment can be well achieved through determining the optimal modal parameters.

Short-term evolution of dynamic characteristics of a RC building under seismic and ambient vibrations

The post-earthquake evaluation of structural integrity is a critical point to be addressed in case of emergency situations triggered by the occurrence of seismic events. A valuable method that can provide important indices to experts performing this operation is the monitoring of structures with seismic sensors that record how the structure responds to earthquake ground motion. In the case of permanent monitoring systems, reliable information can be obtained by comparing the data recorded before, during and after the earthquake, and checking if any abnormal vibrations of the structure or dynamic parameter changes have occurred. The presented study analysed comparatively, for an 11-story reinforced concrete building, vibration data recorded before, during and after the October 28th, 2018 earthquake (MW = 5.5). Continuously recorded data was used to determine the hourly values of the fundamental frequency of the building. The short-term behaviour (72 hours) was assessed, highlighting the modal parameters variation during, before and after the earthquake. In addition, an analysis of the data recorded one and a half hours before the earthquake and one and a half hours after the earthquake provided useful information on the evolution of the building state and on how this “recovered” after the earthquake.

Comparison of Mode Shapes of Carbon-Fiber-Reinforced Plastic Material Considering Carbon Fiber Direction

Previous studies have demonstrated the sensitivity of the dynamic behavior of carbon-fiber-reinforced plastic (CFRP) material over the carbon fiber direction by performing uniaxial excitation tests on a simple specimen. However, the variations in modal parameters (damping coefficient and resonance frequency) over the direction of carbon fiber have been partially explained in previous studies because all modal parameters have only been calculated using the representative summed frequency response function without modal analysis. In this study, the dynamic behavior of CFRP specimens was identified from experimental modal analysis and compared five CFRP specimens (carbon fiber direction: 0°, 30°, 45°, 60°, and 90°) and an isotropic SCS13A specimen using the modal assurance criterion. The first four modes were derived from the SCS13A specimen; they were used as reference modes after verifying with the analysis results from a finite element model. Most of the four mode shapes were found in all CFRP specimens, and the similarity increased when the carbon fiber direction was more than 45°. The anisotropic nature was dominant in three cases of carbon fiber, from 0° to 45°, and the most sensitive case was found in Specimen #3.

Bayesian model updating of a twin-tower masonry structure through subset simulation optimization using ambient vibration data

A Bayesian model updating method using subset simulation optimization given ambient vibration data is proposed to improve the efficiency in sampling and avoid local optimums, which is applied to a full-scale high-rise structure. In the proposed method, the Bayesian fast Fourier transform method is used to extract the most probable values (MPVs) and coefficients of variation (COVs) of modal parameters of the structure, which are considered as the weighting factors in the likelihood function. The posterior probability density function (PDF) of the updating parameters is then derived considering the prior PDF as the regularization term. The subset simulation optimization algorithm is extended to find the global optimal solution of the posterior PDF. The MPVs and COVs of the updating parameters are finally presented. The proposed method is first verified by updating the 15 story stiffness scaling factors of a shear building model. Then, the proposed method is investigated through a numerical application of a four-story frame structure, in which accurate parameter estimations are observed independent of the prior PDF. Finally, the proposed method is applied to a real-world 13-story twin-tower masonry structure which is a modern heritage building. Ambient vibrations were measured through a series of accelerometers instrumented in the structure. The updating parameters are the moduli of elasticity of selected substructures with two model classes studied: three parameters and six parameters. The model-predicted modal parameters from the updated model are in good agreement with their identified counterparts. It is also shown that the case using three parameters provides larger evidence based on the Bayesian model class selection method. The updated refined finite element model provides a basis for the long-term structural health monitoring.

Robust Chatter Stability Prediction of the Milling Process considering Uncertain Machining Positions

Milling stability is a function of the tool point frequency response functions (FRFs), which vary with the movements of the moving parts within the whole machine tool work volume. The position-dependent tool point FRFs result in uncertain prediction of the stability lobe diagram (SLD) for chatter-free machining parameter selection. Taking the variations of modal parameters to represent the variations of tool point FRFs, this paper introduces the edge theorem to predict the robust milling chatter stability. The application of the edge theorem requires the minimum and maximum modal parameters within the machining space defined by the machining position and machining allowance information. Then, radial basis function artificial neural networks (RBFANNs) are used to predict the position-dependent modal parameters in X and Y directions based on the sample information of machining positions and related modal parameters at the tool point. Moreover, sample machining spaces are determined based on the aforementioned sample positions, and the trained RBFANNs are used to obtain corresponding sample extreme modal parameters. On this basis, RBFANNs for predicting the position and machining allowance-dependent extreme modal parameters can also be trained, and they are combined with the edge theorem and zero exclusion condition to calculate robust pairs of the spindle speed (n) and limiting axial cutting depth (aplim) and then plot the robust SLD (RSLD). A case study was performed on a real three-axial vertical machining center, and the plotted RSLD considering position variations was compared with the traditional SLD. Results of the chatter tests show that the RSLD can provide more reliable (ap, n) pairs to guarantee the milling stability, validating the feasibility of the proposed robust milling chatter stability prediction method.

Continuous tracking of bridge modal parameters based on subspace correlations

Modal parameter variation plays an important role in bridge health monitoring. But tracking the long-term variation of modal parameters is restricted by the modal identifiability. Since some modes cannot be identified due to the limitations of sensor locations or excitation conditions, the identified modes will be missing or misclassification in the tracking process. In this paper, the multistage tracking technique based on subspace correlations is proposed. To avoid missing the identified modes, the reference mode list should be complete to cover all identified modes. Thus, the first stage is to update the reference list adaptively, where the correlations between the observability vectors of identified modes and the subspaces of existing reference modes are taken. The second stage is to cluster each traceable mode and the specified reference mode together without misclassification, where the modal similarity is measured by the similarity of observability vectors (SOV). The proposed algorithm is verified by the vibration data of a numerical model and a highway bridge, respectively. The results show that the proposed method can link with modes in the same order correctly and update the reference mode list adaptively to avoid missing the identified modes.

On‐line system identification of structures using wavelet‐Hilbert transform and sparse component analysis

AbstractA new wavelet‐Hilbert transform based sparse component analysis (WHT‐SCA) method is presented for online system identification in indeterminate conditions. The instantaneous phase ratios of output signals are obtained by using a wavelet‐Hilbert transform based filter; and the out‐of‐phase data, that causes errors in identification accuracy, is detected and eliminated. Then, modal parameters of the structure are identified through existing relationships between the dispersion of filtered data in the frequency domain. Subsequently, to demonstrate the capability of the online identification, a new controller is introduced by combining the WHT‐SCA and a semi‐active tuned mass damper (STMD), resulting in creation of smart structures. The performance of the proposed method and controller is investigated through examples. The results demonstrate that, modal parameters of structures are identified accurately even with noise contamination and limited number of sensors. Also, the STMD is effectively robust against any variations in modal parameters of the structure.

Variational mode decomposition based modal parameter identification in civil engineering

An out-put only modal parameter identification method based on variational mode decomposition (VMD) is developed for civil structure identifications. The recently developed VMD technique is utilized to decompose the free decay response (FDR) of a structure into to modal responses. A novel procedure is developed to calculate the instantaneous modal frequencies and instantaneous modal damping ratios. The proposed identification method can straightforwardly extract the mode shape vectors using the modal responses extracted from the FDRs at all available sensors on the structure. A series of numerical and experimental case studies are conducted to demonstrate the efficiency and highlight the superiority of the proposed method in modal parameter identification using both free vibration and ambient vibration data. The results of the present method are compared with those of the empirical mode decomposition-based method, and the superiorities of the present method are verified. The proposed method is proved to be efficient and accurate in modal parameter identification for both linear and nonlinear civil structures, including structures with closely spaced modes, sudden modal parameter variation, and amplitude-dependent modal parameters, etc.

Automated Modal Analysis for Tracking Structural Change during Construction and Operation Phases.

The automated modal analysis (AMA) technique has attracted significant interest over the last few years, because it can track variations in modal parameters and has the potential to detect structural changes. In this paper, an improved density-based spatial clustering of applications with noise (DBSCAN) is introduced to clean the abnormal poles in a stabilization diagram. Moreover, the optimal system model order is also discussed to obtain more stable poles. A numerical simulation and a full-scale experiment of an arch bridge are carried out to validate the effectiveness of the proposed algorithm. Subsequently, the continuous dynamic monitoring system of the bridge and the proposed algorithm are implemented to track the structural changes during the construction phase. Finally, the artificial neural network (ANN) is used to remove the temperature effect on modal frequencies so that a health index can be constructed under operational conditions.

Vibration‐Based Damage Assessment in Gravity‐Based Wind Turbine Tower under Various Waves

In this study, the feasibility of vibration‐based damage assessment in a wind turbine tower (WTT) with gravity‐based foundation (GBF) under various waves is numerically investigated. Firstly, a finite element model is constructed for the GBF WTT which consists of a tower, caisson, and foundation bed. Eigenvalue analysis is performed to identify a few vibration modes of interest, which represent complex behaviors of a flexible tower, rigid caisson, and deformable foundation. Secondly, wave‐induced dynamic pressures are analyzed for a few selected wave conditions and damage scenarios are also designed to simulate the main components of the target GBF WTT. Thirdly, forced vibration responses of the GBF WTT are analyzed for the wave‐induced excitation. Then modal parameters (i.e., natural frequencies and mode shapes) are extracted by using a combined use of time‐domain and frequency‐domain modal identification methods. Finally, the variation of modal parameters is estimated by measuring relative changes in natural frequencies and mode shapes in order to quantify the damage‐induced effects. Also, the wave‐induced variation of modal parameters is estimated to relatively assess the effect of various wave actions on the damage‐induced variation of modal parameters.

Dynamic Property Evaluation of a Long-Span Cable-Stayed Bridge (Sutong Bridge) by a Bayesian Method

Modal identification aims at identifying the dynamic properties including natural frequency, damping ratio, and mode shape, which is an important step in further structural damage detection, finite element model updating, and condition assessment. This paper presents the work on the investigation of the dynamic characteristics of a long-span cable-stayed bridge-Sutong Bridge by a Bayesian modal identification method. Sutong Bridge is the second longest cable-stayed bridge in the world, situated on the Yangtze River in Jiangsu Province, China, with a total length of 2 088[Formula: see text]m. A short-term nondestructive on-site vibration test was conducted to collect the structural response and determine the actual dynamic characteristics of the bridge before it was opened to traffic. Due to the limited number of sensors, multiple setups were designed to complete the whole measurement. Based on the data collected in the field tests, modal parameters were identified by a fast Bayesian FFT method. The first three modes in both vertical and transverse directions were identified and studied. In order to obtain modal parameter variation with temperature and vibration levels, long-term tests have also been performed in different seasons. The variation of natural frequency and damping ratios with temperature and vibration level were investigated. The future distribution of the modal parameters was also predicted using these data.

Motion-based design of TMD for vibrating footbridges under uncertainty conditions

Tuned mass dampers (TMDs) are passive damping devices widely employed to mitigate the pedestrian-induced vibrations on footbridges. The TMD design must ensure an adequate performance during the overall life-cycle of the structure. Although the TMD is initially adjusted to match the natural frequency of the vibration mode which needs to be controlled, its design must further take into account the change of the modal parameters of the footbridge due to the modification of the operational and environmental conditions. For this purpose, a motion-based design optimization method is proposed and implemented herein, aimed at ensuring the adequate behavior of footbridges under uncertainty conditions. The uncertainty associated with the variation of such modal parameters is simulated by a probabilistic approach based on the results of previous research reported in literature. The pedestrian action is modelled according to the recommendations of the Synpex guidelines. A comparison among the TMD parameters obtained considering different design criteria, design requirements and uncertainty levels is performed. To illustrate the proposed approach, a benchmark footbridge is considered. Results show both which is the most adequate design criterion to control the pedestrian-induced vibrations on the footbridge and the influence of the design requirements and the uncertainty level in the final TMD design.

Identification of the time-varying modal parameters of a spacecraft with flexible appendages using a recursive predictor-based subspace identification algorithm

This study focuses on the recursive identification of the time-varying modal parameters of on-orbit spacecraft caused by structural configuration changes. For this purpose, an algorithm called recursive predictor-based subspace identification is applied as an alternative method to improve the computational efficiency and noise robustness, and to implement an online identification of system parameters. In the existing time-domain identification methods, the eigensystem realization algorithm and subspace identification methods are usually applied to obtain the on-orbit spacecraft modal parameters. However, these approaches are designed based on a time-invariant system and singular value decomposition, which require a significant amount of computational time. Thus, these methods are difficult to employ for online identification. According to the adaptive filter theory, the recursive predictor-based subspace identification algorithm can not only avoid the singular value decomposition computation but also provide unbiased estimates in a general noisy framework using the recursive least squares approach. Furthermore, in comparison with the classical projection approximation subspace tracking series recursive algorithm, the recursive predictor-based subspace identification method is more suitable for systems with strong noise disturbances. By establishing the dynamics model of a large rigid-flexible coupling spacecraft, three cases of on-orbit modal parameter variation with time are investigated, and the corresponding system frequencies are identified using the recursive predictor-based subspace identification, projection approximation subspace tracking, and singular value decomposition methods. The results demonstrate that the recursive predictor-based subspace identification algorithm can be used to effectively perform an online parameter identification, and the corresponding computational efficiency and noise robustness are better than those of the singular value decomposition and projection approximation subspace tracking series approaches, respectively. Finally, the applicability of this method is also verified through a numerical simulation.

Effects of high winds on a long-span sea-crossing bridge based on structural health monitoring

This paper focuses on the effects of high winds on vibrational responses and modal parameter's variation for a unique sea-crossing cable-stayed bridge, i.e. Donghai Bridge, based on the long-term structural health monitoring (SHM) data. This bridge is located in a typhoon-prone area of the northwestern Pacific Ocean, and 80% of the vehicles traversing it are heavy-load container trucks. The relative influence of high winds and heavy-load traffic on the structural vibration responses is investigated by a comparison of typical operational cases. The high wind dominates in the girder's lateral vibration of Donghai Bridge, while the girder's vertical and torsional accelerations are more sensitive to heavy-load traffic rather than high winds. Also, the frequency band of the wind excitation is lower than that of traffic load. During high winds, the modal parameters of this bridge are relatively difficult to stably identify, thereby leading to a well-pronounced discreteness of the parameters' estimates. This paper could serve as a field evidence for the wind-resistant design and the performance evaluation of bridges in similar operational conditions.

Fatigue damage detection and prediction of fatigue life on a cantilever beam

Purpose Fatigue failure is an important criterion to be considered in the design of structures and mechanical components. Catastrophic failure of structures in service conditions can be avoided using adequate techniques to detect and localize fatigue damage. Modal analysis is a tool used in mechanical and structural engineering to estimate dynamic properties and also to monitor the health of structures. If modal analysis is applied periodically to a structure, fatigue damage can be detected and localized and the fatigue life can be extended by means of suitable reinforcement and repairing. The paper aims to discuss these issues. Design/methodology/approach The experimental results corresponding to the fatigue tests carried out on a steel S-275 cantilever beam are presented. Operational modal analysis was applied periodically to the beam in order to study the variation of modal parameters during the tests and the stresses were estimated combining a numerical model and the acceleration modal coordinates measured at discrete points of the structure. The experimental results are compared with those predicted applying the S-N model of Eurocode 3. Findings A methodology that combines a finite element model and the experimental responses of a structure has been applied to estimate the stress time histories of a cantilever beam clamped to a foundation through a steel plate. The estimated stresses have been used to predict the fatigue damage according to the Eurocode 3. Due to the fact that no information of the scatter is provided by this code (EC3), only the number of cycles corresponding to a probability of failure of 5 percent can be predicted. Originality/value The proposed methodology can be applied to real structures in order to know the accumulated fatigue damage in real time.