Random Vibration Signals Research Articles

Thermal-biomechanical manikin applied in turbulent airflow and vibration systems in transient conditions

This paper applied a thermal-biomechanical manikin in turbulent airflow and vibration systems in transient conditions. This numerical model evaluated the thermal and biomechanical components to which the human body is subjected. The first one considers the first-order equations systems based on the thermal numerical model, while the second one considers the second-order equations systems based on the vibration numerical model. This second-order equations system is converted into a first-order equation system. The resolution of the thermal and biomechanical numerical models is made through the Runge-Kutta-Fehlberg method with error control. The thermal numerical model is used in the study of the steady-state and transient conditions when the skin is subjected to mean and turbulent airflow. The biomechanical numerical model is used in the study of the human body vibrations applied to the feet, that a standing person is subjected, using periodical and random vibration signals of the floor. The thermal analysis shows that with an air fluctuation velocity, the skin temperature reduces slightly. The amplitude of the vibration in the lower body section is higher than in the upper body section. The introduction of the randomised vibration, in the periodical vibration, the human body vibration increases the fluctuation level.

Mechanical-computing metastructure for self-powered vibration sensing

Triboelectric nanogenerator-based vibration sensors (TVSs) present a promising approach for online vibration monitoring, offering early detection of excessive vibrations that pose risks to the functionality of devices and infrastructure. However, the structural design of most current TVSs lacks consideration for information processing capabilities, resulting in limited detection bandwidth and displacement signal fidelity. This study first introduces a quasi-zero-stiffness (QZS) mechanical-computing metastructure aimed at enhancing the structural intelligence of TVSs and extending their vibration signal detection bandwidth. The optimization of the QZS metastructure involved adjusting the length ratio and inclination angle of the zero-order polynomial beam to achieve ultra-low resonant frequencies. The results indicate that the TVS based on the mechanical-computing metastructure (MCM-TVS) is capable of efficiently detecting complex random signals, achieving an average measurement accuracy above 85 % for the spectral components of random vibration signals. Furthermore, the sensor exhibited remarkable linearity (99 %) in measuring vibration amplitude and maintained consistent sensitivity (with less than 25.8 % fluctuation), facilitating the lossless conversion of displacement to electrical signals. Consequently, this novel approach of incorporating an MCM into TVS design offers substantial insights for the advancement of high-performance vibration signal monitoring.

PSD estimation and modal parameter identification for random vibrations with blade tip timing measurement

Abstract Blade tip timing (BTT) is a vibration measurement technique for blade health monitoring. Most of the existing BTT analysis methods are suitable for deterministic vibration signals but are ineffective for random vibration signals that often occur in practice. Statistical analysis of BTT data is significant for random vibration analysis and improving blade monitoring efficiency. This study proposes a compressive model for power spectral density (PSD) estimation and modal parameter identification. The efficiencies of three compressive sensing algorithms, including the least absolute shrinkage and selection operator (Lasso), nonnegative least squares (NLS), and nonnegative orthogonal matching pursuit, are compared. The effects of the duration of the signal and the frequency resolution on the quality of the estimated PSD and the identified parameters are discussed. According to the analysis, to obtain accurate damping ratios, it is recommended that the duration of the signal be greater than 3000 revolutions. A Q criterion based on the half-power bandwidth is proposed to determine the set of frequency resolutions. Numerical and field tests were conducted to verify the proposed method. The results indicate that the NLS algorithm is recommended to use. The root-mean-square errors of the identified natural frequencies and damping ratios obtained by the proposed method were 0.065 Hz and 0.023%, respectively. The proposed method was verified at different rotational speeds in a field test, demonstrating the capability of the method over a wide rotational speed range and providing more opportunities to detect blade damage.

Modified time domain randomization technique for multi-shaker non-stationary non-Gaussian random vibration control

Traditional random vibration environmental tests simulate stationary Gaussian random vibration environments. In this work, the generation and closed-loop control of multi-shaker non-stationary non-Gaussian random vibration signals with the modified time domain randomization technique are studied. The amplitude modulation function is introduced to control the non-stationary and non-Gaussian characteristics that the root mean square value of the generated signal changes with time. The kurtosis relationship between the one frame pseudo-random signal and consecutive true random signal is derived theoretically. It is found that the kurtosis of the consecutive non-stationary random signal is determined by the amplitude modulation function and kurtosis of the pseudo-random signal. The standard deviation of the time-varying root mean square reflects the non-stationary characteristics of the generated signal. A control strategy for multi-shaker non-stationary non-Gaussian random vibration environmental test is proposed. The non-stationary and non-Gaussian characteristics are extracted from the measured response signals so that the power spectral densities, kurtoses and non-stationary characteristics can be controlled simultaneously. The results from the simulation examples and multi-shaker vibration experiments prove the feasibility and practicability of the proposed non-stationary non-Gaussian random signal generation method and control strategy.

Random vibration-based progressive fatigue damage monitoring in thermoplastic coupons: a preliminary investigation

In recent years there has been an increasing trend towards the utilization of composites, particularly thermoplastics, in various components of aerostructures. The prelusion of such materials has underscored the significance of investigating their fatigue behavior and developing reliable methods for detecting fatigue damage. In this context, vibration-based techniques hold significant potential as they leverage the inherent excitation provided by in-flight noise and turbulence. This study aims at assessing the progressively accumulated fatigue damage in thermoplastic coupons via random vibration signals while accounting for operational and inter-structural uncertainties. The experimental process consists of preliminary tension and fatigue tests, interrupted fatigue tests, C-Scan inspection tests, and non-contact random vibration tests. Consecutive fatigue states are obtained by performing fatigue tests at intervals of 10 000 cycles for a population of 7 coupons. At each interruption, ultrasonic C-Scan and vibration inspection tests are performed, allowing for the visualization of fatigue damage and random vibration signal analysis. Welch Power Spectral Density estimates are employed and are shown to have good potential for distinguishing among different fatigue states despite the inevitable population and experimental uncertainty. Furthermore, fatigue damage is found to progress symmetrically and laterally along the free edges of the test coupons, which is explained by the free edge effect.

LQG/LTR based robust youla parameterized adaptive vibration control for the supporting platform of rotating liquid mirror

In mechatronic systems, the vibrations which commonly consist of band-limited random signals mixed with large multiple narrow-band deterministic signals may negatively impact the system performance. For example, due to the incomplete matching of the mechanism and the rotation of the motor, random and deterministic vibration disturbance may occur in the supporting platform of the rotating liquid mirror. In this paper, a robust Youla ( Q) parameterized adaptive regulation approach has been proposed to minimize such kind of vibration signals for the rotating platform system with model uncertainties. Firstly, the inner-loop robust controller with linear quadratic Gaussian with loop transfer recovery ( LQG/LTR) is optimally designed by choosing the suitable weighting functions to achieve the trade-off between robust stability and control performance to deal with random vibration signals. Then the Youla parameter is augmented to construct a set of Q-parameterized stabilizing controllers, and the robust stability of the system is analyzed through dual-Youla parameterization of the uncertain model. The recursive least squares (RLS) adaptive algorithm is developed to tune the Q parameter online to construct a desired adaptive controller for further residual vibration elimination. An experimental evaluation of the controller in reducing the vibration of the supporting platform of a rotating liquid mirror has been carried out, and the results illustrate that the proposed adaptive robust vibration regulation approach can effectively suppress the band-limited random and narrow-band deterministic vibration signals.

Robust early detection of hunting on railway vehicles: single-sensor based methods and critical comparisons

ABSTRACT The problem of robust and early detection of railway hunting is considered and two single-sensor ‘dynamics-based’ methods employing adaptive Recursive AutoRegressive (RAR) modelling of the car-body lateral random vibration signal are postulated. The first is based on a Degree-of-Stochasticity (DS) measure of the vibration signal and the second on the minimum underlying Damping Ratio (DR). Fully automated tuning for both methods is achieved via Bayesian optimization. The performance of the methods is systematically assessed via high numbers of Monte Carlo simulations under various Scenarios employing a high-fidelity SIMPACK-based vehicle model and three performance criteria: the True Positive Rate (TPR), the False Positive Rate (FPR), and the Detection Delay Time (DDT) with respect to conventional hunting initiation. The results reveal very good performance and robustness to suspension faults and worn track conditions for both methods, with the DR-based exhibiting an edge. Its performance and achievable robustness are also shown to be clearly superior to those of three alternative methods.

An Architecture for On board Frequency Domain Analysis of Launch Vehicle Vibration Signals

The dynamic properties of the airborne structures plays a crucial role in the stability of the vehicle during
 flight. Modal and spectral behaviour of the structures are simulated and analysed. Ground tests are carried out with environmental conditions close to the flight conditions, with some assumptions. Subsequently, based on the flight telemetered data, the on-board mission algorithm and the auto-pilot filter coefficients are fine tuned. An attempt is made in this paper to design a novel architecture for analysing the modal and spectral random vibration signals on-board the flight vehicle and to identify the dominant frequencies. Based on the analysed results, the mission mode algorithm and the filter coefficients can be fine tuned on-board for better effectiveness in control and providing more stability. Three types of windows viz. Hann, Hamming and Blackman-Harris are configured with a generalised equation using FIR filter structure. The overlapping of the input signal data for better inclusiveness of the real-time data is implemented with BRAM. The domain conversion of the data from time domain to frequency domain is carried out with FFT using Radix-2 BF architecture. The FFT output data are processed for calculating the power spectral density. The dominant frequency is identified using the array search method and Goldschmidt algorithm is utilised for the averaging of the PSDs for better precision. The proposed architecture is synthesised, implemented and tested with both Synthetic and doppler signal of 300 Hz spot frequency padded with Gaussian white noise. The results are highly satisfactory in identifying the spot frequency and generating the PSD array.

Retracted: Research on Numerical Simulation Method of Nonstationary Random Vibration Signal Sensor in Railway Transportation

Retracted: Research on Numerical Simulation Method of Nonstationary Random Vibration Signal Sensor in Railway Transportation

PSD characteristics for the random vibration signals used in bridge structural health monitoring in Vietnam based on a multi-sensor system

This study proposes two parameters, including the appearance frequency of harmonics (AFH) and the change in shape of the power spectral density (PSD), which are examined to assess the decline in stiffness of a bridge span. PSDs are obtained from the real vibration signals of the randomized traffic load model based on accelerometer multi-sensors that indicate the change in mechanical behavior of the structure over time. In addition, AFHs evaluate the workability of the structure. With these parameters in mind, actual vibrations in real beam structures are studied with the aim of using structural health monitoring to assess the bearing capacity reduction on Saigon Bridge’s spans. The results show that AFHs and the high-frequency regions relate to the decreased stiffness of the bridge’s spans over a given period of time. In the future, this research can be used to monitor structural health for various types of structure materials and many different bridge spans.

A Modal Frequency Estimation Method of Non-Stationary Signal under Mass Time-Varying Condition Based on EMD Algorithm

A method to estimate modal frequency based on empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD) is proposed. This method can decrease the difficulties in identifying modal frequency of combine harvesters. First, we used 16 acceleration sensors installed at different test points to collect vibration signals of a corn combine harvester under operating conditions (mass time-varying conditions). Second, we calculated mean value, variance and root mean square (RMS) value of the vibration signals, and analyzed its stationarity of vibration signals. Third, the main frequencies of the 16 points were extracted using the EMD and EEMD methods. Finally, we considered modal frequencies identified by the SSI algorithm as standard, and calculated the fitting degrees of the EMD and EEMD methods. The results show that in different time periods (0~60 s and 60~120 s), the maximum differences of the mean value, variance and RMS value of signals were 0.8633, 171.1629 and 11.3767, and the vibration signal under the operating condition of field harvesting can be regarded as a typical non-stationary random vibration signal. The EMD method had more modal aliasing than EEMD, and when we obtained the fitting equations of EMD, EEMD and SSI methods, the value of the Euler distance between the EMD fitting equation and the SSI fitting equation was 446.7883, while that for EEMD and SSI was 417.2845. The vibration frequencies calculated by the EEMD method is closer to the modal frequencies identified by SSI algorithm. The proposed method provides a reference for modal frequency identification and vibration control in a complex working environment.

Vibration-based and computer vision-aided nondestructive health condition evaluation of rail track structures

In railway engineering, monitoring the health condition of rail track structures is crucial to prevent abnormal vibration issues of the wheel–rail system. To address the problem of low efficiency of traditional nondestructive testing methods, this work investigates the feasibility of the computer vision-aided health condition monitoring approach for track structures based on vibration signals. The proposed method eliminates the tedious and complicated data pre-processing including signal mapping and noise reduction, which can achieve robust signal description using numerous redundant features. First, the method converts the raw wheel–rail vibration signals directly into two-dimensional grayscale images, followed by image feature extraction using the FAST-Unoriented-SIFT algorithm. Subsequently, Visual Bag-of-Words (VBoW) model is established based on the image features, where the optimal parameter selection analysis is implemented based on fourfold cross-validation by considering both recognition accuracy and stability. Finally, the Euclidean distance between word frequency vectors of testing set and the codebook vectors of training set is compared to recognize the health condition of track structures. For the three health conditions of track structures analyzed in this paper, the overall recognition rate could reach 96.7%. The results demonstrate that the proposed method performs higher recognition accuracy and lower bias with strong time-varying and random vibration signals, which has promising application prospect in early-stage structural defect detection.

Research on Numerical Simulation Method of Nonstationary Random Vibration Signal Sensor in Railway Transportation

During railway transportation, due to various factors such as road conditions and operating conditions and produced vibrations and shocks, this kind of vibration environment may cause fatigue damage to on-board equipment and transported goods. The authors propose a research on the numerical simulation method of the nonstationary random vibration signal sensor of railway transportation; first, they establish the mathematical model of the railway nonstationary random vibration signal sensor and then introduce the method of reconstructing the railway nonstationary random vibration signal sensor. For railway nonstationary non-Gaussian random vibration reconstruction signal, compare the time-domain characteristics of the sampled signal, and for railway nonstationary non-Gaussian random vibration reconstruction signal, compare the frequency domain characteristics of the sampled signal. The results show that the relative error of the RMSM function is within 6%, the relative error of the sliding bias function is within 10%, and the relative error of the sliding kurtosis function is within 8%. The energy distribution of the edge Hilbert amplitude spectrum is very similar, with absolute error less than 6%. The energy fluctuations are similar in each band, with absolute error rates less than 4% in most bands. The method proposed in this article, suitable for reconstruction of railway nonstationary Gaussian random vibration and nonstationary non-Gaussian vibration signal sensor, verifies the effectiveness and feasibility of the signal reconstruction method. The model and signal reconstruction method proposed in this paper are applied to the railway nonstationary Gaussian and nonstationary non-Gaussian random vibration sampling signals.

Fatigue life prediction based on modified narrowband method under broadband random vibration loading

The vibration fatigue life and vibration response signal at the dangerous position of each specimen were obtained by the broadband random vibration fatigue test for 7075-T651 aluminum alloy, and the stress amplitude probability distribution of vibration response signal was counted by rainflow counting method. By comparing the probability density distribution functions of broadband random vibration signal by frequency-domain method and analyzing the fitting accuracy of different distribution models for rainflow distribution, a new model for frequency-domain fatigue life prediction based on modified narrowband distribution model was proposed. The proposed model takes the second-order spectral width parameter of vibration signal as the weight coefficient, and the life prediction results are more accurate and less dispersive.

Track segment automated characterisation via railway–vehicle–based random vibration signals and statistical time series methods

The feasibility of automated railway track segment characterisation, as part of a broader track condition based maintenance procedure, is explored via railway–vehicle–based random vibration signals and Statistical Time Series (STS) methods. In particular, three methods within a Multiple Model (MM) framework, which are founded on data-driven stochastic parametric models for the representation of the partial vehicle-rail dynamics, are employed. The random vibration signals are obtained from two sensors, which are mounted on the axlebox and the bogie frame, respectively, of an Athens Metro railway vehicle moving under three different speeds (60, 70 or 80 km/h). The performance assessment of the methods is based on two distinct track characterisation problems. The first corresponds to the characterisation of a specific track segment after 6 months of continuous use, while the second to the comparison between two nominally identical track segments which were installed with a 2 month time interval and are used by different numbers and types of trains. The results indicate deterioration of the track segment in the first characterisation problem and differences between the two nominally identical segments in the second. The superiority of the employed methods over a state-of-the-art method is also demonstrated via proper comparisons.

Multi-site damage precise localization via the random vibration functional model based method: Formulation & concept validation

The postulation and experimental validation of a random vibration data based Functional Model Based Method (FMBM) for multi-site damage localization, involving the determination of the number of damage locations and interval estimation of their coordinates, in presented. The method is based on Functional Models (FMs), along with proper statistical decision making and estimation techniques, and is capable of working with a limited number of random vibration signals under normal operating conditions. Two distinct versions of the method are introduced: A Forward or Multiple Model version which is based on multiple Functional Models, and a Backward or Single Model version based on a single counterpart. Both versions are experimentally validated and compared via hundreds of single- and double-site damage scenarios on the wing of a lab-scale aircraft skeleton structure, while a sensitivity analysis examining performance degradation for reduced numbers of training vibration signals is also undertaken. The results indicate high effectiveness in both determining the number of damage sites and estimating their precise coordinates along with their associated uncertainty.

Technologies for Monitoring the Dynamics of Damage Development in Drilling Rigs Using High-Order Moments of the Noise

The paper deals with the development of algorithms for calculating the high-order moments of the noise of noisy signals and their use in the analysis of the technical condition of industrial facilities. It is shown that for monitoring and controlling the onset of an emergency at oil production facilities, random vibration signals are used, which, in addition to the noise caused by external factors at the time of the initiation of the malfunction, also contain additional noise. The characteristics of this noise contain certain information about the technical condition of the drilling rig. Earlier, algorithms were developed for calculating the variance, standard deviation, and density distribution function of the noise that cannot be separated from the noisy signal. In this paper, it is shown that high-order moments of the noise can be used as a diagnostic indicator for determining the presence and degree of damage development in drilling rigs during the latent period of damage initiation. Possible options for calculating the high-order moments of the noise are analyzed. Recursive algorithms are developed for expressing high-order moments of a normally distributed noise through its variance. The possibility of calculating the high-order moments of the noise through the distribution density functions is also shown. A matrix consisting of estimates of the high-order moments of the noise calculated at different instants of time is built. It is shown that at the first stage, it is possible to determine the presence and degree of the damage based on the values of the matrix elements. At the second stage, the intensity of damage development is determined by comparing the values of the noise characteristics at different instants of time. Calculations are performed for all signals coming from the sensors. Training is carried out and, the correspondence is established between the values of the high-order moments and degrees and intensity of damage development. The possibility of using the proposed algorithms and technologies in the system of noise control of the beginning and development dynamics of accidents at drilling rigs is shown. It is noted that even if the estimates of the high-order moments of the sum noisy vibration signals change within a wide range during drilling, their high-order noise moments do not exceed a predetermined value in the absence of a malfunction. In the event of a malfunction, the estimates of the highorder moments of the noise exceed the predetermined threshold level and, as the defect develops, their values also change. If adverse processes are stabilized, the variation of these estimates stops as well. Moreover, depending on the degree and intensity of stabilization of the technical condition of the drilling rig, the change in the estimates of the moments, starting from the highest to the lowest or vice versa, stops one by one. This specific feature of estimates of high-order noise moments of vibration signals allows us to identify the beginning and to control the development dynamics of the latent period of an emergency state of the drilling process.

Semi-actively Controllable Vehicle Seat Suspension System with Negative Stiffness Magnetic Spring

This article proposes an innovative controllable seat suspension with a long stroke negative stiffness (NS) spring for reducing the whole-body vibration of heavy vehicle drivers. The proposed seat suspension is mainly composed of a NS magnetic spring (NSMS), a coil spring, and an electromagnetic damper for semiactive vibration control. In this way, the system characteristic induced by the NSMS can be maximally utilized to improve ride comfort. Property tests are conducted to validate the mathematical modeling and the constructed system stiffness characteristic. Based on the derived dynamic model, a prescribed performance control technique with closed-loop stability is employed to guarantee both the transient and steady-state responses under the predefined levels. Experiments are implemented where the transient and random vibration signals are applied on the seat suspension base. The results illustrate that when compared with a commercial seat product, an increasing convergence rate by 16% and a decreasing frequency-weighted root-mean-square value by 34% are achieved.

Quantitative diagnosis method of beam defects based on laser Doppler non-contact random vibration measurement

The beam structure is prone to defect damage during its use, and the rapid quantitative diagnosis of the beam structure can detect the defects of the beam in real time and quantitatively. In this article, the method of obtaining the vibration time-domain signal under random excitation of beam structure is proposed by using random vibration excitation and Laser Doppler principle. Based on this, the defect quantitative identification algorithm of beam structure is proposed based on fast Fourier, continuous wavelet transform and convolutional neural network. The random vibration of different parts of steel beams with artificial defects is measured by Laser Doppler method. The experimental results show that the defect size of the beam structure can be effectively identified only by the random vibration signal of the finite point. The method is expected to help to develop an online real-time assessment instrument for beam structure defects in service state.

Operational Modal Analysis of Transformer Windings

Broadband responses under random excitations can reflect the modal characteristics of a structure. This paper investigates the applicability of operational modal analysis (OMA) to extract modal parameters of transformer windings under random excitations. Firstly, random vibration signals are extracted from measured vibration signals by estimating an accurate power frequency and eliminating vibration harmonics. Then, modal characteristics are obtained by applying OMA to the extracted random vibration signals. The numeric study on a winding axial vibration model demonstrates the effectiveness of the proposed method in obtaining its modal characteristics. Laboratory experiments show that the natural frequencies calculated by OMA are a subset of the actual natural frequencies of windings and the tank. The field test results of a 110 kV power transformer show that the number of natural frequencies increase when winding deformation occurs. OMA of transformer windings may pave a way for online winding condition monitoring.