Structural Modal Frequencies Research Articles

Output-only identification of time-varying structural modal parameters under thermal environment

Obtaining the input load presents a significant challenge for system identification problems with time-varying characteristics in aerospace engineering. Therefore, the modal parameter is determined through output-only identification techniques. Considering rapid time-varying characteristics in thermal environment, a Recursive Subspace Method (RSM) is used to enhance the precision of identifying modal parameters. A three-degree-of-freedom system with time-varying stiffness is first investigated to validate the identification method. The effect of noise on the robustness of the algorithm is discussed. Then, the experimental investigation is undertaken considering a composite beam under a time-varying thermal environment though the thermal-vibration experimental system. Experimental results indicate that the change of structural modal frequencies under variable temperature environment is mainly affected by the thermal stress induced in the structure. Comparing the experimental and simulation result, the output-only identification approach has good efficiency and convergence for time-varying system.

Structure failure analysis on metro axle-box hanger due to modal resonance with rail corrugation

During the long-term service of a metro vehicle, different kinds of fracture failure occur on the bogie, with the axle-box hanger being a representative one. To investigate the cause of the hanger structure failure, a study was conducted that combined field investigation with finite element analysis, focusing on the modal resonance behavior between the hanger and the rail corrugation. Based on the findings, a structural optimization of the hanger was proposed and an experimental verification was conducted. The results show that the main reason for the hanger fracture failure is that the resonance phenomenon that occurred in the hanger structural modal frequency when exposed to the rail corrugation, leading to the poor lateral vibration environment of the hanger and the fracture failure in the long-term service operation. The first-order structural modal frequency of the hanger is 432 Hz, which is very close to the wheel/rail excitation frequency of 435 Hz caused by the rail corrugation. The modal frequency of three newly designed hangers can prevent the frequency caused by the rail corrugation. Experimental verification of the new hangers showed a 55.49% lower maximum average acceleration of hanger lateral vibration compared to the original structure, confirming the effectiveness of the redesigned hangers.

Correlation Analysis of Large-Span Cable-Stayed Bridge Structural Frequencies with Environmental Factors Based on Support Vector Regression

The dynamic characteristics of bridge structures are influenced by various environmental factors, and exploring the impact of environmental temperature and humidity on structural modal parameters is of great significance for structural health assessment. This paper utilized the Covariance-Driven Stochastic Subspace Identification method (SSI-COV) and clustering algorithms to identify modal frequencies from four months of acceleration data collected from the health monitoring system of the Jintang Hantan Twin-Island Bridge. Furthermore, a correlation analysis is conducted to examine the relationship between higher-order frequency and environmental factors, including temperature and humidity. Subsequently, a Support Vector Machine Regression (SVR) model is employed to analyze the effects of environmental temperature on structural modal frequencies. This study has obtained the following conclusions: 1. Correlation analysis revealed that temperature is the primary influencing factor in frequency variations. Frequency exhibited a strong linear correlation with temperature and little correlation with humidity. 2. SVR regression analysis was performed on frequency and temperature, and an evaluation of the fitting residuals was conducted. The model effectively fit the sample data and provided reliable predictive results. 3. The original structural frequencies underwent smoothing, eliminating the influence of temperature-induced frequency data generated by the SVR model. After eliminating the temperature effects, the fluctuations in frequency within a 24 h period significantly decreased. The data presented in this paper can serve as a reference for further health assessments of similar bridge structures.

A Field Investigation of Stability Characteristics of Pressure Fluctuation and Vibration in Prototype Pump Turbine at Multiple Working Points

In practical operation, pump turbines typically operate far from their designed working points, which has a significant impact on the stability of the unit’s operation. In this paper, we conducted a field test to investigate the stability characteristics of prototype pump turbines at different working points. By adjusting the given power of the generator in a stepwise manner to control its working point, we obtained the statistical and spectral characteristics of pressure signals and acceleration signals. In turbine mode, the result shows that, at low, medium, and high power, the variation in pressure fluctuation characteristics is influenced by three different factors, while vibration generally reaches its maximum value at approximately 50 MW. In pump mode, variations in pressure were observed among different measurement points in the low-frequency range, and the characteristics of vibration acceleration were influenced by both the rotor–stator interaction (RSI) and the structural modal frequencies. We emphasized that the high-frequency bands have influences on the unit comparable in magnitude to those of the rotor–stator interaction, which has rarely been mentioned in previous studies. Through detailed testing and analysis of the unit’s actual operation, we can gain a better understanding of its behavior and performance in the turbine and pump modes, and these results hold significant importance for ensuring the stability and reliability of the unit.

A modal estimation method of rotating blade based on compressed sensing and blade tip timing

Structural modal estimation has consistently remained one of the most crucial areas of research in mechanical vibration analysis and signal processing. It is imperative to accurately monitor the vibration signals of rotor blades and their corresponding structural modal parameters. Blade tip timing (BTT) is a promising approach used to measure vibration and monitor the health of blades. However, most existing BTT methods focus on frequency accuracy, neglecting damping, a key physical quantity that represents the strength of the structure. This research focuses on damping modal estimation of blade vibration and proposes a sparse reconstruction algorithm based on a two-dimensional Laplace wavelet family, which addresses the inherent under-sampled problem of BTT technology while enabling estimations of both the structural modal frequency and modal damping of the blades. Firstly, the proposed algorithm is achieved by designing a Laplace wavelet dictionary based on prior information and using a convex optimization objective function with a regularization term. Secondly, Laplace wavelet dictionary matches the signal better than the traditional Fourier dictionary based on the similarity between the damped vibration signal and the Laplace wavelet, then a sparser representation vector can be obtained. Moreover, the research object is not limited to a single blade, but can be easily expanded to multiple stages and multiple rotating blades monitored simultaneously. Finally, the simulation and physical test results indicate that the proposed method exhibits high reconstruction accuracy, reliability, and anti-noise abilities.

A Master Multi-Slave System Based on Structural Modal Frequencies

Structural Health Monitoring (SHM) is a process where, through sensors-based electronic systems and output data analysis, the structural integrity of a building or an infrastructure is observed and determined through periodically sampled measurements for material and geometric variations, ensuring safety and minimizing risk factors. Over the years, the approach to this problem evolved both in terms of system technology, with the use of more accurate sensors, and the parameters used to determine the building status, i.e., the extraction of the damage index. In these terms, structural modal harmonics-based analysis is acquiring more and more relevance. In this paper, we propose a fully custom master multi-slave system used for SHM purposes, capable of acquiring data from six different channels coming from two independent accelerometers suitably configured as to synchronously produce spectrograms and static trim of the monitored structure. A test of the system has been performed on a modular structure subject to random perturbation. Time and frequency domain results were analyzed before and after structural alterations. Their effects were studied in a 500 Hz bandwidth, showing a drift in the resonant frequency of the structure from 145 Hz to 152 Hz, and, additionally, a harmonic displacement: medium-frequency components experienced a 50 Hz drift, while low-frequency components collapsed into two harmonics at 60 Hz and 90 Hz. These tests proved the system’s functionality and the feasibility of this method for structural integrity analysis and, eventually, damage evaluation.

Hypersonic Fluid–Thermal–Structural Interaction of Cone–Slice–Ramp: Computations with Experimental Validation

The paper presents an investigation of fluid–thermal–structural interaction (FTSI) on a complex geometry in hypersonic flows. The objective is to assess high-fidelity numerical tools for FTSI by validating two numerical frameworks against wind-tunnel data. We choose a cone–slice–ramp geometry with a wedge angle of 30 deg subjected to a laminar inflow at Mach 8. First, the time-averaged and the time-resolved laminar flow solutions are validated and highlight the mean flow features and their unsteady characteristics, including low-frequency bubble breathing and shear-layer flapping at a higher frequency. The numerical analysis reveals the presence of upstream and downstream legs of streamwise vortices. Next, FTSI analysis is performed at a tractable computational cost by decomposing the numerical frameworks into a quasi-steady FTSI (QS-FTSI) analysis and a transient fluid–structure interaction (FSI) analysis based on the disparity of the characteristic timescales. The QS-FTSI results highlight the shear-layer reattachment as the dominant source heating the structure, with nonuniform spanwise variations due to the streamwise vortices. The temperature increase drives the decrease in the structural modal frequencies. The FSI analysis was performed for an unheated, undeformed structure and a nominal heated and deformed structure. The average error in the predicted FSI frequency of the unheated panel is 2.65% in comparison to the experimental data; however, this value increases to 7.42% for the heated panel. The frequency peaks are associated with the structural mode shapes via dynamic mode decomposition analysis and show a close resemblance to natural modes, indicating weak FSI coupling. The FTSI study concludes that for a cone–slice–ramp configuration under the present inflow conditions, the interaction mostly occurs in a one-way coupled manner, where the flowfield drives the thermal and structural response of the panel.

Influence of external load on forced vibration of rectangular plate

Rectangular plate is one typical structure with wild application in engineering, and the force vibration is the basis for analysis of sound radiation of plate. In this work, numerical simulation is conducted for force vibration of rectangular plate, and the influence of external load is also studied. Numerical results show that, the rectangular plate will resonate under external load at certain driven frequency, and it’s strictly related to structural modal frequencies. Structural vibration response will change obvious with the change of location of external load. When the location is fixed, with the increase of action region of external load, the acceleration of plate will decrease and some new resonance frequencies will be observed. Conclusions here will lay foundation for further work on sound radiation of plate.

A hybrid-attention-ConvLSTM-based deep learning architecture to extract modal frequencies from limited data using transfer learning

This paper leverages each pixel of a picture acquired from a video camera, in which structural dynamic information is contained, in order to decompose spatiotemporal information from such a non-contact virtual sensor array in the same way as traditional accelerometers to extract structural modal frequencies. Attention-based deep neural network architecture is proposed in this work to better visualize the dynamic properties of structures in the existence of noise with a high resolution. The work combines CNNs and Recurrent Neural Networks (RNNs) to predict modal frequencies of structures from a series of consecutive images. High discriminative features of video frames are firstly extracted using the CNN, and then Conv-Long Short-Term Memory (ConvLSTM) is applied to further process the extracted features to capture the temporal dynamics in videos. The attention mechanisms are embedded in the network to ensure the model learns to focus selectively on those frames containing system dynamics. In particular, the proposed computer vision-based deep learning model takes the video of a vibrating structure as the input and successfully estimates the modal frequencies. Transfer learning is applied to cohere the knowledge learned from publicly available datasets to a much more sophisticated structure and estimate the resonant frequencies. The proposed algorithm optimizes the filter design for video processing in a fully automated way without any human intervention and can generalize and transfer that learned information to more complex structures. The model is trained using publicly available generic baseline data (Dataset A) consisting of several simple beam structures with different material properties and sizes and transferred the learned knowledge to unseen data (Dataset B) consisting of an independent turbine blade. It is concluded that the newly proposed method is more autonomous, accurate, and capable of generalizing the model to a new independent dataset using a transfer learning strategy, and the most advantage of the proposed approach is that the trained deep learning architecture has the capability of estimating the resonant frequencies for independent structures and extending the resonant frequency estimations to higher modes.

Eliminating environmental and operational effects on structural modal frequency: A comprehensive review

Eliminating environmental and operational effects on structural modal frequency: A comprehensive review

Numerical investigation of an insect-scale flexible wing with a small amplitude flapping kinematics

To maintain flight, insect-scale air vehicles must adapt to their low Reynolds number flight conditions and generate sufficient aerodynamic force. Researchers conducted extensive studies to explore the mechanism of high aerodynamic efficiency on such a small scale. In this paper, a centimeter-level flapping wing is used to investigate the mechanism and feasibility of whether a simple motion with a certain frequency can generate enough lift. The unsteady numerical simulations are based on the fluid structure interaction (FSI) method and dynamic mesh technology. The flapping motion is in a simple harmonic law of small amplitude with high frequency, which corresponds to the flapping wing driven by a piezoelectric actuator. The inertial and aerodynamic forces of the wing can cause chordwise torsion, thereby generating the vertical aerodynamic force. The concerned flapping frequency refers to the structural modal frequency and FSI modal frequency. According to the results, we find that under the condition that frequency ratio is 1.0, that is, when the wing flaps at the first-order structural modal frequency, the deformation degree of the wing is the highest, but it does not produce good aerodynamic performance. However, under the condition that frequency ratio is 0.822, when the wing flaps at the first-order FSI modal frequency, the aerodynamic efficiency achieve the highest and is equal to 0.273. Under the condition that frequency ratio is 0.6, that is, when the wing flaps at a frequency smaller than the first-order FSI modal frequency, the flapping wing effectively utilizes the strain energy storage and release mechanism and produces the maximum vertical coefficient which is equal to 4.86. The study shows that this flapping motion can satisfy the requirements of lift to sustain the flight on this scale.

On Using Kriging Response Surface Method for EV Battery Pack Structural Response Prediction and Mass Optimization

Structural response of battery packs in electric vehicles when subjected to road loads is an important factor that decides its performance and life during normal operation. In this paper a kriging response surface model is built using a Design of Experiment (DOE) run dataset to predict structural response and global modal frequency metrics of the battery pack. Using this Response Surface Model (RSM), we can rapidly optimize the battery pack design with respect to structural response and achieve significant mass reduction. This method reduces turnaround times for design optimization in early stages of battery pack design.

Damage Detection of Tension Pendulums in Cable-Stayed Bridges Using Structural Frequency Variance

Structural health monitoring represents an efficient way to diagnose the condition of cable-stayed bridges. Most studies assessing the condition of cable-stayed bridges and detecting damage to them have been developed to monitor the longitudinal performance of bridge bearings. However, few studies have aimed to detect the damage to tension pendulums, which are usually tie-down cables that resist girder uplift from auxiliary piers. This study aims to develop an effective method for detecting the damage of tension pendulums in cable-stayed bridges using structural modal frequencies. First, the sensitivity of the bridge frequency to tension pendulum damage is derived according to the Rayleigh method. Then, a finite-element simulation of a cable-stayed bridge is conducted to validate the rationality of the frequency index. Finally, a case study on tension pendulum damage is carried out for the cable-stayed Yonghe Bridge. The results indicate that the frequency change is far more sensitive to the damage of the tension pendulums than to the damage of the stay cables. The failure of tie-down cables will result in a substantial decrease in the bridge frequency, up to approximately 35% for the first vertical bending mode of the bridge. In practice, the damage of tension pendulums can be effectively detected by a sudden decrease in the measured frequency of cable-stayed bridges.

Combining GNSS and accelerometer measurements for evaluation of dynamic and semi-static characteristics of bridge structures

With the increasing number of long span bridges, real-time, accurate and continuous monitoring of their safety is important at present. This study investigates the combination of a global navigation satellite system (GNSS) and accelerometer for monitoring dynamic and semi-static characteristics of bridge structures. A field experiment was conducted with the integration of a GNSS and accelerometer. Considering the noise interference of GNSS monitoring, performance tests were first conducted in different environments to investigate the noise characteristics. Next, complete ensemble empirical mode decomposition with adaptive noise-wavelet packet (CEEMDAN-WP) algorithm was chosen for denoising, among which a double criterion based on the correlation coefficient and effective coefficient was proposed to sift the intrinsic mode functions. After the noise reduction process, structural dynamic displacements and modal frequencies were successfully extracted from the 50 Hz GNSS real-time kinematic (GNSS-RTK) and accelerometer data, in which the displacements presented a consistent trend and the first natural frequency was the same (i.e. 0.369 Hz). Structural semi-static characteristics were evaluated by using 1 Hz (RTK), post-processed kinematic, and precise point positioning data. With reference to relevant specifications, the structural failure probability of the bridge in the vertical direction was calculated to be 0.4319. The results indicate that GNSS-RTK is reliable in monitoring structural dynamic and semi-static displacements of the bridge. Additionally, the proposed improved CEEMDAN-WP with double criterion is effective for background noise reduction. In addition, there may be some non-adequate behaviors, such as heavy traffic and vehicle overload, leading to the critical operation of the bridge.

Embedded Streaming Principal Components Analysis for Network Load Reduction in Structural Health Monitoring

Principal component analysis (PCA) is a well-established approach commonly used for dimensionality reduction. However, its computational cost and memory requirements hamper the adoption of PCA in heavily resource-constrained embedded platforms. Streaming approaches have been proposed that may enable embedded implementations of the PCA. Among them, the history PCA (HPCA) algorithm stands out for its robustness to the variability in parameters and accuracy. This article presents a parallel and memory-efficient implementation of HPCA in a structural health monitoring (SHM) application based on a heterogeneous network with sensor nodes measuring three-axial accelerations and gateways collecting measurements from several nodes and sending them to the cloud storage and analytic facility. In the targeted application, standard PCA reaches $15\times $ compression factor with an average reconstruction signal-to-noise ratio of 16 dB and a negligible impact on the accuracy in the tracking of structural modal frequencies. By embedding HPCA on our SHM network gateways, we achieve the same compression factor as standard PCA, with more than $1000\times $ reduction in data memory footprint for running the algorithm. Furthermore, we parallelize HPCA on the gateway, and we achieve a speedup of $7.1\times $ (on 8 cores). Finally, we explore a fixed-point HPCA implementation on sensors (network end nodes), that maximally distributes compression workload, minimizes required communication bandwidth, and maintains the same quality of reconstruction as HPCA in floating point, with a compression factor of $10\times $ .

Analysis of belt bridge mode and blasting vibration response spectrum in a mine

With the wide application of blasting technology, people pay more and more attention to the impact of blasting vibration on the surrounding environment and buildings. To blasting vibration analysis and evaluation of the effect on the stability of the skip shaft, belt bridge based on the large finite element analysis software ANSYS Workbench entity unit model, the belt of the bridge structure modal frequency and applying 2 cm/s numerical simulation of blasting vibration load was the response of the study. The calculation results show that the maximum stress value is 0.0063 MPa, belt bridge in belt bridge at the top of the column, in the concrete design tensile strength of 1.43 MPa. The maximum strain of the belt bridge is 5.05×10-8, which is within the allowable elastic deformation range of the building, and is far less than the ultimate tensile strain of C40 concrete 1×10-4. The skip well is in a stable state.

Field measurement study on time-varying characteristics of modal parameters of super high-rise buildings during super typhoon

This study identifies the modal parameters of four super high-rise buildings in Shenzhen and analyzes the variation of their structural dynamic properties with amplitude and time based on the long-term field data of Super Typhoon Mangkhut. Results show the maximum acceleration of the four buildings is 13.29–41.96 milli-g and occurs at the maximum wind speed period. In the early stage, as the wind speed increases with time, structural modal frequencies decrease and reach the minimum during the maximum wind speed period. Subsequently, wind speed gradually decreases, modal frequencies increase slowly, and the highest ratio of frequency change is 11.9%. The change of damping ratio is somewhat stochastic but overall first increases and then decreases with time. The mode shapes of most buildings remain basically unchanged during typhoon. However, the mode shapes of the building with the maximum response differ greatly at the maximum and the low wind speeds. Besides, the two-order modal frequencies drop sharply near the maximum wind speed and approach one another to an indistinguishable degree. These new results and rules of modal parameters have important reference values for the further research on the influence of wind–structure interaction on structural wind effect and subsequent wind-induced vibration control.

Multichannel processing of vibrational measurements: A constrained subspace application.

Monitoring mechanical systems operating in uncertain environments contaminated with both environmental disturbances and noise lead directly to low signal-to-noise-ratios, creating an extremely challenging processing problem, especially in real-time. In order to estimate the performance of a particular system from uncertain vibrational data, it is necessary to identify its unique resonant (modal) frequency signature. The monitoring of structural modes to determine the condition of a device under investigation is essential, especially if it is a critical entity of an operational system. The development of a model-based scheme capable of the on-line tracking of the inherent structural modal frequencies by applying both constrained subspace identification techniques to extract the modal frequencies and state estimation methods to track the evolution is discussed. An application of this approach to a cylindrical structural device (pipe-in-air) is analyzed based on theoretical simulations along with controlled validation experiments, including injected anomalies illustrate the approach and performance. Statistics are gathered to bound potential processors for real-time performance employing these constrained techniques.

A hybrid ant lion optimizer with improved Nelder–Mead algorithm for structural damage detection by improving weighted trace lasso regularization

Structural damage detection is the kernel technique in deploying structural health monitoring. The structural damage–detection technique using heuristic algorithms has been developed at an astounding pace over the past years. However, some existing structural damage–detection methods are prone to easily fall into the local optimum and to be unstable when they are applied to complex structures. In order to make full use of advantages of heuristic algorithms and overcome abovementioned shortcomings, a hybrid algorithm, which combines the ant lion optimizer with an improved Nelder–Mead algorithm, is proposed to solve the constrained optimization problem of complex structural damage detection. First, an objective function is established for damage identification using structural modal parameters, that is, frequencies and mode shapes. The solution to the objective function is accurately attained by a newly improved weighted trace lasso which can improve the computing performance and stability of procedure and reduce randomness of weighted coefficients. After assessing the computing performance of the proposed hybrid algorithm using three classical mathematical benchmark functions, two structural damage–detection numerical simulations and a laboratory verification are then conducted to fully assess the structural damage–detection capability of the proposed method. Meanwhile, the equivalent element stiffness-reduction model is introduced to estimate the real damage severities of cracks which are created in laboratory structures and to compare with the structural damage–detection results by the proposed method. The illustrated results show that the proposed hybrid algorithm can locate damage and quantify damage severity more accurately and stably with a good robustness to noise.

Application of the Hilbert–Huang transform to identify the dynamic characteristics of a caisson foundation during liquefaction

This paper presents the application of a Hilbert–Huang transform data processing technique in a dynamic response analysis to identify the dynamic characteristics of a caisson foundation during liquefaction. The degradation of structural modal frequencies during liquefaction under strong earthquakes directly related to a reduction in the stiffness of the soil-foundation structure due to the loss of strength, and the nonlinearity of the liquefied soil layer always occur in a short time. Thus, the short-duration variation of frequencies provided a good indicator for the occurrence of the liquefaction and geometric distortion of a soil foundation system during strong earthquakes and was a very important step in the structural health monitoring work of foundation structures. This study shows that the proposed approach was effective in identifying the instantaneous downshift of frequency of caisson foundation system during liquefaction. This study was based on the measured acceleration response data of a test foundation model from a 1-G shaking table test. Additionally, 2D numerical modeling using a total stress analysis stipulated in the highway bridge specification (JRA 2002), an equivalent linear method in the liquefaction calculation of foundation, was conducted to evaluate the consistency with vibration testing.