Modal Frequency Prediction of Chladni Patterns Using Machine Learning

The introduction of machine learning (ML) in the research domain is a new era technique. The machine learning algorithm is developed for frequency predication of patterns that are formed on the Chladni plate and focused on the application of machine learning algorithms in image processing. In the Chladni plate, nodes and antinodes are demonstrated at various excited frequencies. Sand on the plate creates specific patterns when it is excited by vibrations from a mechanical oscillator. In the experimental setup, a rectangular aluminum plate of 16 cm x 16 cm and 0.61 mm thickness was placed over the mechanical oscillator, which was driven by a sine wave signal generator. 14 Chladni patterns are obtained on a Chladni plate and validation is done with modal analysis in Ansys. For machine learning, a large number of data sets are required, as captured around 200 photos of each modal frequency and around 3000 photos with a camera of all 14 Chladni patterns for supervised learning. The current model is written in Python language and model has one convolution layer. The main modules used in this are Tensor Flow Keras, NumPy, CV2 and Maxpooling. The fed reference data is taken for 14 frequencies between 330 Hz to 3910 Hz. In the model, all the images are converted to grayscale and canny edge detected. All patterns of frequencies have an almost 80% - 99% correlation with test sample experimental data. This approach is to form a directory of Chladni patterns for future reference purpose in real-life application. A machine learning algorithm can predict the resonant frequency based on the patterns formed on the Chladni plate.

IDENTIFICATION OF TIME-VARYING MODAL PARAMETERS USING LINEAR TIME-FREQUENCY REPRESENTATION

A new method of parameter identification based on linear time-frequencyrepresentation and Hubert transform is proposed to identity modal parameters of linear time-varyingsystems from measured vibration responses. Using Gabor expansion and synthesis theory, measuredresponses are represented in the time-frequency domain and modal components are reconstructed bytime-frequency filtering. The Hilbert transform is applied to obtain time histories of the amplitudeand phase angle of each modal component, from which time-varying frequencies and damping ratios areidentified. The proposed method has been demonstrated with a numerical example in which a lineartime-varying system of two degrees of freedom is used to validate the identification scheme based ontime-frequency representation. Simulation results have indicated that time-frequency representationpresents an effective tool for modal parameter identification of time-varying systems.

Identifying the relationship between suspension parameters of underframe equipment and carbody modal frequency

As a critical component of the railway vehicle, underframe equipment has a great influence on the ride comfort of railway vehicles due to their big mass and active vibration. Therefore, study on the relationship between suspension parameters of underframe equipment and the modal frequency of carbody is extremely crucial for con trolling the ride quality of railway vehicles. In this paper, a finite element model of the carbody was developed to investigate the effects of the suspension location, the mass of the suspension equipment, and the suspension frequency on the mode of the carbody. Then, the matching relationship between the suspension parameters and the modal frequency of the carbody was studied through the transfer function. In addition, roller rig tests were performed to verify the numerical simulation model of the carbody. The results show that the suspension parameters of the underframe equipment have a great influence on the mode of the carbody, especially for the frequency of the first bending mode. To improve the frequency of carbody highfrequency bending and reduce energy transfer, equipment with a large mass should be suspended toward the middle of the carbody. The weight of the equipment strongly affects the first bending frequency and energy transfer of the carbody. The frequency of heavy suspended equipment should be sufficiently low to increase the transmissibility of high frequencies and improve the vibration characteristics of the carbody. Although the bending frequency of the carbody can be improved effec tively by increasing the suspension stiffness of thesuspension equipment, in order to reduce carbody vibration effectively, the suspension frequency of the equipment should be slightly lower than the carbody bending frequency.

An operational modal analysis method in frequency and spatial domain

A frequency and spatial domain decomposition method （FSDD） for operational modal analysis （OMA） is presented in this paper, which is an extension of the complex mode indicator function （CMIF） method for experimental modal analysis （EMA）. The theoretical background of the FSDD method is clarified, Singular value decomposition is adopted to separate the signal space from the noise space. Finally, an enhanced power spectrum density （PSD） is proposed to obtain more accurate modal parameters by curve fitting in the frequency domain. Moreover, a simulation case and an application case are used to validate this method.

A refined Frequency Domain Decomposition tool for structural modal monitoring in earthquake engineering

Output-only structural identification is developed by a refined Frequency Domain Decomposition（rFDD） approach, towards assessing current modal properties of heavy-damped buildings（in terms of identification challenge）, under strong ground motions. Structural responses from earthquake excitations are taken as input signals for the identification algorithm. A new dedicated computational procedure, based on coupled Chebyshev Type Ⅱ bandpass filters, is outlined for the effective estimation of natural frequencies, mode shapes and modal damping ratios. The identification technique is also coupled with a Gabor Wavelet Transform, resulting in an effective and self-contained time-frequency analysis framework. Simulated response signals generated by shear-type frames（with variable structural features） are used as a necessary validation condition. In this context use is made of a complete set of seismic records taken from the FEMA P695 database, i.e. all 44 ＂Far-Field＂（22 NS, 22 WE） earthquake signals. The modal estimates are statistically compared to their target values, proving the accuracy of the developed algorithm in providing prompt and accurate estimates of all current strong ground motion modal parameters. At this stage, such analysis tool may be employed for convenient application in the realm of Earthquake Engineering, towards potential Structural Health Monitoring and damage detection purposes.

Numerical Approach to Simulate the Effect of Corrosion Damage on the Natural Frequency of Reinforced Concrete Structures

Corrosion of reinforcing steel in concrete elements causes minor to major damage in different aspects.It may lead to spalling of concrete cover,reduction of section’s capacity and can alter the dynamic properties.For the dynamic properties,natural frequency is to be a reliable indicator of structural integrity that can be utilized in non-destructive corrosion assessment.Although the correlation between natural frequency and corrosion damage has been reflected in different experimental programs,few attempts have been made to investigate this relationship in forward modeling and/or structural health monitoring techniques.This can be attributed to the limited available data,the complex nature of corrosion,and the involvement of multidisciplinaryfields.Therefore,this study presents a numerical attempt to simulate the effect of corrosion damage on the natural frequency of the structure.The approach relies on simulating the time history response of the structure using a modified Bouc-Wen model that incorporates the nonlinear effects of corrosion.Then,modal analysis is utilized to assess the change in dynamic properties in the frequency domain.Tofinish up,regression algorithms are employed tofind optimal relationship between involved parameters,including corrosion damage as input,and natural frequency as output.The efficiency of the suggested framework is illustrated in thirteen buildings with cantilevered column lateral force-resisting system and different levels of corrosion.

Output only modal identification and structural damage detection using time frequency & wavelet techniques

The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom （MDOF） linear time invariant （LTI） and linear time variant （LTV--due to damage） systems based on Time-frequency （TF） techniques--such as short-time Fourier transform （STFT）, empirical mode decomposition （EMD）, and wavelets--is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform （HT） approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they arc signal based; hence, can be used for output only modal identification. A three degree of freedom 1：10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration （white noise） response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.

Monitoring the Modal Frequency and Velocity Variations of Bridges under Ambient Excitation

We conducted a long-term monitoring experiment on the Lutuanxilu Bridge located in Changping District of Beijing, employing our recently developed real-time bridge monitoring system based on the Guralp CMG-6TD broadband seismometer. We identified the modal parameters with the stochastic subspace identification( SSI) algorithm,and continuously monitored the temporal velocity variation with coda wave interferometry.The results show that:( 1) the highly sensitive Guralp CMG-6TD broadband seismometer,which records the three-component vibration signal within broad frequency range,is well suited for long-term bridge health monitoring.( 2) With the continuous vibration signal from ambient excitation,the stochastic subspace algorithm can robustly identify the low-order modal parameters and the coda wave interferometry can accurately monitor the tiny velocity variation.( 3) The elastic modulus of bridge materials changes significantly associated with varying temperature,leading to diurnal velocity variation with amplitude of approximately 1%. The velocity variation shows strong negative correlation with temperature fluctuation. Meanwhile,the modal frequencies remain quite stable,suggesting that the velocity variation may be a more sensitive quantitative damage index.( 4) While the modal frequencies reflect the integrated health status of the bridge,the velocity variation can be utilized to monitor the local elastic modulus. Therefore,it is crucial for bridge health monitoring to continuously monitor the two key damage indexes under ambient excitation.

Microwave frequency downshift in the time-varying collision plasma

Microwave frequency downshift in the time-varying collision plasma has been demonstrated by particle-in-cell simulations.The simulation results are consistent with the theoretical analysis,and the preconditions for microwave frequency downshift are that the collision frequency needs to be greater than the incident wave frequency,and the plasma frequency is two times greater than the incident wave frequency.Finally,the simulation results are compared with the reported experimental results indicating good agreement.

Coupled vibrations and frequency shift of compound system consisting of quartz crystal resonator in thickness-shear motions and micro-beam array immersed in liquid

The dynamic characteristics of a quartz crystal resonator（QCR） in thicknessshear modes（TSM） with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inviscid and incompressible for simplicity. Dynamic equations of the coupled system are established. The added mass effect of liquid on micro-beams is discussed in detail. Characteristics of frequency shift are clarified for different liquid depths. Modal analysis shows that a drag effect of liquid has resulted in the change of phase of interaction（surface shear force）, thus changing the system resonant frequency. The obtained results are useful in resonator design and applications.

Effect of Cell Size on the Fundamental Natural Frequency of FRP Honeycomb Sandwich Panels

In the present work, the effect of hexagonal cell size of the core on the fundamental natural frequency of FRP honey-comb sandwich panels has been analyzed both experimentally and by finite element technique. Experimental Modal tests were conducted on hexagonal cell honeycombs ranging in size from 8 mm to 20 mm maintaining the facing thickness constant at around 1mm with two different boundary conditions viz C-F-F-F and C-F-C-F. The traditional “strike method” has been used to measure the vibration properties. The modal characteristics of the specimens have been obtained by studying its impulse response. Each specimen has been subjected to impulses through a hard tipped hammer which is provided with a force transducer and the response has been measured through the accelerometer. The impulse and the response are processed through a computer aided FFT Analyzing test system in order to extract the modal parameters with the aid of software. Theoretical investigations have been attempted with appropriate assumptions to understand the behavior of the honeycomb sandwich panels during dynamic loading and to validate experimental results. Finite Element modeling has been done treating the facing as an orthotropic laminate and Core as orthotropic with different elastic constants as recommended in the literature. The results are presented which show that the theoretical model can accurately predict the fundamental frequency and how honeycombs with difference cell size will perform under dynamic loads.

Assessment of structural damage using natural frequency changes

The present paper develops a new method for damage localization and severity estimation based on the employment of modal strain energy. This method is able to determine the damage locations and estimate their severities, requiring only the information about the changes of a few lower natural frequencies. First, a damage quantification method is formulated and iterative approach is adopted for determining the damage extent. Then a damage localization algorithm is proposed, in which a damage indicator is formulated where unity value corresponds to the true damage scenario. Finally, numerical studies and model tests are conducted to demonstrate the effectiveness of the developed algorithm.

Rigid Bridges Health Dynamic Monitoring Using 100 Hz GPS Single-Frequency and Accelerometers

This article presents the modal frequency recordings of a rigid bridge, monitored by the GPS receivers (Global Positioning System) with a data recording rate of 100 Hz and accelerometers. The GPS data processing was performed through the double-difference phase, using the adjusted interferometry technique (i.e. phase residue method—PRM&reg). In the method, the double-difference phase of the carrier L1 is realized by using two satellites only, one was positioned at the zenith of the structure and the other satellite was positioned near the horizon. The results of the parametric adjustment of the PRM observations were finalized through software Interferometry, mathematical algorithm were applied and compared with the accelerometer. The comparison served to validate the use of GPS as a fast and reliable instrument for the preliminary monitoring of the dynamic behavior of the bridge, road artworks which are common in several countries, especially in the Brazilian road network. The data time series from the GPS and accelerometers were processed using the Wavelet. The detection of frequencies means that the combination of 100 Hz GPS receivers and the PRM allows detecting vibrations up to 5 mm. It presented significant results which were never obtained by the Fourier Transform.

Complex Modal Analysis for the Time-Variant Dynamical Problem of Rotating Pipe Conveying Fluid

A semi-analytical form of complex modal analysis is proposed for the time-variant dynamical problem of rotating pipe conveying fluid system.The complex mode superposition method is introduced for the dynamic analysis in the time and frequency domains,in which appropriate orthogonality conditions are constructed to decouple the time-variant equation of motion.Consequently,complex frequencies and modes of vibration are analytically formulated and the variations of frequencies and damping of the system are evaluated.Numerical time-variant example of rotating pipe conveying fluid illustrates the effectiveness and accuracy of this method.Furthermore,the proposed solution scheme is also applicable to other similar time-variant dynamical problems.

Identification of Time-Varying Modal Parameters for Thermo-Elastic Structure Subject to Unsteady Heating

A time-varying modal parameter identification method combined with Bayesian information criterion(BIC)and grey correlation analysis(GCA)is presented for a kind of thermo-elastic structures with sparse natural frequencies and subject to an unsteady temperature field.To demonstrate the method,the thermo-elastic structure to be identified is taken as a simply-supported beam with an axially movable boundary and subject to both random excitation and an unsteady temperature field,and the dynamic outputs of the beam are first simulated as the measured data for the identification.Then,an improved time-varying autoregressive(TVAR)model is generated from the simulated input and output of the system.The time-varying coefficients of the TVAR model are expanded as a finite set of time basis functions that facilitate the time-varying coefficients to be time-invariant.According to the BIC for preliminarily determining the scope of the order number,the grey system theory is introduced to determine the order of TVAR and the dimension of the basis functions simultaneously via the absolute grey correlation degree(AGCD).Finally,the time-varying instantaneous frequencies of the system are estimated by using the recursive least squares method.The identified results are capable of tracking the slow time-varying natural frequencies with high accuracy no matter for noise-free or noisy estimation.

Damage Detection of Offshore Jacket Structures Using Frequency Domain Selective Measurements

损坏察觉技术为的发展近海夹克衫结构是重要的阻止灾难的事件。这份报纸使用频率回答为监视的结构的健康的目的基于的方法。在完成这项任务的努力，最小的等级不安理论的概念被利用了。现在的文章介绍有希望的方法论有效地选择频率点。达到这个目标，每个成员的形式的紧张精力比率在结构的不同自然频率被评估以便为损坏察觉识别敏感频率领域。建议方法论开创大得多的察觉效率的可能性。另外，建议方法的表演在与多重损坏的关系被评估。上述的点用二个维的夹克衫平台的数字学习被说明，并且结果证明了令人满意利用建议方法论。

A review of mid-frequency vibro-acoustic modelling for highspeed train extruded aluminium panels as well as the most recent developments in hybrid modelling techniques

The present paper reviews the vibro-acoustic modelling of extruded aluminium train floor structures including the state-of-the-art of its industrial applications, as well as the most recent developments on mid-frequency mod- elling techniques in general. With the common purpose to predict mid-frequency vibro-acoustic responses of stiffened panel structures to an acceptable accuracy at a reasonable computational cost, relevant techniques are mainly based on one of the following three types of mid-frequency vibro- acoustic modelling principles： （1） enhanced deterministic methods, （2） enhanced statistical methods, and （3） hybrid deterministic/statistical methods. It is shown that, although recent developments have led to a significant step forward in industrial applicability, mature and adequate prediction tech- niques, however, are still very much required for solving sound transmission through, and radiation from, extruded aluminium panels used on high-speed trains. Due to their great potentials for predicting mid-frequency vibro-acoustics of stiffened panel structures, two of recently developed mid-frequency modelling approaches, i.e. the so-called hybrid finite element-statistical energy analysis （FE-SEA） and hybrid wave-based method- statistical energy analysis （WBM-SEA）, are then recapitulated.

结构动力学应用中若干基本概念的研究

结构动力特性被广泛应用于结构振动控制、结构可靠性设计和健康监测,由此涉及到一些动力学基本概念的理解问题尚待深入探讨。采用一简支梁横向振动算例以及分别通过模态位移法和模态加速度法对多自由度系统的响应振幅进行分析计算,探讨结构位移响应与第一阶固有频率的关系、结构各阶位移模态的贡献与模态应变能的关系。基于模态正交性,通过分析多自由度振动系统的位移响应,论述了系统共振的必要条件,即在保证系统振动频率(某阶固有频率)等于激励频率的同时,其位移响应还应呈现出相应模态的形态;实现多自由度系统纯模态共振,可用于精确识别结构的模态参数。

基于多模态神经网络的微地震事件检测

针对微地震有效信号时序特征存在的局限导致微地震事件识别准确率不高的问题,提出了一种基于多模态学习的神经网络微地震事件检测方法。首先,利用道集数据的相关性以目标道为轴对称制作多道时域模态,对目标道进行时频分析得到S域模态特征;然后,联合时域模态和S域模态设计微地震事件检测神经网络,综合多模态的特征进行训练学习,提高微地震事件识别的精度;最后,为验证方法的有效性,对合成微地震信号进行低信噪比数据分析、小幅值数据分析以及实际油井微地震监测信号事件分析。结果表明,该方法可以有效检测低信噪比及微弱的微地震事件;与支持向量机、卷积神经网络、基于监督机器学习方法的对比实验结果表明该方法具有更高的抗噪性与准确率。

基于空耦超声激励的微结构模态频率温度特性研究

为了研究微悬臂结构弯曲振动模态频率的温度特性,首先针对各向异性材料的等截面矩形微悬臂结构建立了其各阶模态频率温度系数的理论模型;然后搭建了包括激光测振单元、空耦超声激励单元和温度控制单元的非接触式微结构动态特性测试系统;最后利用所搭建的测试系统分别对等截面矩形单晶硅微悬臂梁在室温~300℃时的动态特性进行了测试,获得了微悬臂梁前三阶弯曲振动模态频率随温度的变化规律和频率温度系数。研究结果表明,单晶硅微悬臂梁前三阶弯曲振动模态频率随着温度的升高而呈近似线性的减小,并且微悬臂梁前三阶弯曲振动模态具有几乎相同的频率温度系数,其中一阶模态频率的温度系数为-2.18×10-5/℃,二阶模态频率的温度系数为-1.91×10^(-5)/℃,三阶模态频率的温度系数为-2.01×10^(-5)/℃,前三阶模态频率温度系数的测试结果与理论模型预测值的偏差分别3×10^(-7)/℃,3×10^(-6)/℃和2×10^(-6)/℃。