Acceleration Power Spectral Density Research Articles

A model-based approach for joint estimation of track irregularities and track support modulus from trackside measurements in railway turnouts

ABSTRACT The paper proposes a model-based approach for the concomitant estimation of track modulus, track irregularity, and dynamic loading by combining an analytical model of a beam on an elastic foundation with vibration data collected by a trackside measurement system. The model is empirically extended to incorporate the effects of dynamic wheel/rail interaction forces when both short wavelength defects (in the rail surface) and medium-long wavelength track irregularities (e.g. hanging sleepers, differential ballast settlement) are present. The power spectral density of the rail vertical acceleration is then exploited in combination with the extended model to estimate track parameters using least squares. The proposed method is validated on vibration data collected in a turnout of the Danish railway infrastructure over a period of 2.5 years. The obtained results show that changes over time in track modulus and track irregularities, and consequently in dynamic wheel/rail contact forces, can be efficiently monitored from trackside measurements.

Transfer Function-Based Road Classification for Vehicles with Nonlinear Semi-Active Suspension

Ride comfort and handling are two important criteria regarding vehicle vibration control. For solving the inconsistency between ride comfort and handling, a semi-active suspension system equipped with a road classification system can be a suitable solution. Because the road condition varies during driving, the control gain of the semi-active suspension system should be adaptively changed according to the road level. In this paper, accelerometer data and a transfer function scheme will be used for road classification, and there is no need to measure the road directly with difficult and often expensive methods. In this approach, a transfer function that makes relevant the Power Spectral Density (PSD) of the road surface and the PSD of car acceleration is used. Road classification is investigated for a vehicle with a nonlinear, semi-active suspension system equipped with Continuous Damping Control (CDC) and nonlinear springs. To show the applicability of the proposed method in scenarios close to real situations, robustness analysis is done by considering vehicle model uncertainties and sensor noise. The simulation results show that the proposed method is robust against typical uncertainties and accelerometer noise and can classify the road level, which is used to tune the parameters of the nonlinear, semi-active suspension system.

Study on the Dynamics Characteristics of HTS Maglev Train Considering the Aerodynamic Loads under Crosswinds

High-temperature Superconducting (HTS) maglev trains are vulnerable to the effects of crosswinds when operating at high speeds in open-air conditions, potentially compromising riding comfort and safety. This study established a vehicle dynamic model based on the nonlinear maglev-track relationship and added aerodynamic loads under crosswinds to the train’s simplified load center to address this issue. Using the maximum vibration acceleration limit and the Sperling index, we evaluated the riding comfort of the HTS maglev train under different conditions. Further, the vibration acceleration power spectral density was analyzed to reveal the impact of increasing the train’s operating speed and crosswind speed. The results indicated that the lateral and vertical Sperling index achieved an “excellent” rating, even at crosswind speeds of up to 20.7 m/s when the train was traveling at speeds of up to 600 km/h. However, it was noted that particular attention should be given to the riding comfort in the head car when the speed reaches 600 km/h. Moreover, the influence of the increase in train speed on the vibration frequency domain distribution of the three car bodies and the train’s riding comfort is greater than that of the increase in the crosswind speed. These findings may provide a valuable reference for the future engineering application of the HTS maglev train.

Deep-SVDD-based Real-time Early Warning for Cable Structure

Cables are essential load-bearing components in many structures, and early warning methods are crucial for ensuring their safety. Early warning methods based on structural dynamic responses have played a key role due to their low cost, easy maintenance, and replaceability. However, extracting robust damage-sensitive features from dynamic responses under ambient excitation remains challenging. In this paper, an early warning method based on deep support vector data description is proposed. The method extracts damage features from the power spectral density of lateral acceleration of cables and interpretable damage indicators are proposed for identifying cable interaction. The proposed unsupervised learning method only requires healthy state lateral acceleration data for model training. Numerical and field experiments on the Shanghai-Suzhou-Nantong Yangtze River Bridge demonstrate the method's effectiveness in early warning for cables. Compared to the deep auto-encoder based damage diagnosis method, the proposed method shows higher accuracy and potential for real-time early warning of cable structures.

Effects of different vibration spectrum shapes on mechanical damage of postharvest Huangguan pear during transportation

Mechanical damage of the horticultural produce during postharvest transportation is an important criteria for fruit sorting and grading. The vibration during transportation has a significant effect on the mechanical damage of the fruit. In this study, the effect of different vibration spectrum shapes on mechanical damage of Huangguan pear (Pyrus bretschneideri Rehd, cv. Huangguan) was investigated. Four acceleration spectrums (spectrum Ⅰ, spectrum Ⅱ, spectrum Ⅲ, and spectrum Ⅳ) with same vibration level and different shapes were evaluated. The power spectral density (PSD) amplitude in the resonant region was in the order of spectrum Ⅰ > spectrum Ⅱ> spectrum Ⅲ > spectrum Ⅳ. The change in appearance, physiological properties (respiratory rate and weight loss), and mechanical properties (firmness and elastic modulus) of the pears were evaluated after vibration. Results showed that vibration resulted in quality deterioration of pear. Compared to the control group, respiratory rate and weight loss of the pears increased while the flesh firmness and elastic modulus of the pears decreased after vibration. The mechanical damage became more serious as stacked position increased. The effect of spectrum shape on the mechanical damage of pear was also obvious. Different degree of mechanical damage was observed under spectrum Ⅰ, spectrum Ⅱ, spectrum Ⅲ, and spectrum Ⅳ vibration. The higher the acceleration PSD in resonant region, the more serious the mechanical damage of pear. In comparison with the control group, pear under spectrum Ⅰ effect showed the most mechanical damage and the pear under spectrum Ⅳ effect had the minimum mechanical damage. Furthermore, S−Grms curves (damage area - vibration level) showed a clockwise rotation from spectrum Ⅰ to Ⅲ vibration. This study reveals the mechanical damage mechanism of pears based on acceleration spectrum shape and provides guidance for postharvest loss reduction using simulated test.

Performance study of semi-active seat suspension added by quasi-zero stiffness structure under various vibratory roller models

To enhance the vibratory roller’s comfort, three different types of seat suspension including the seat’s semi-active suspension system (SASS) controlled by the FLC-PID controller, seat’s passive suspension system (PSS) added by the quasi-zero stiffness structure (QZSS), and seat’s SASS added by the QZSS are proposed. Three different vehicle dynamic models including a one-dimensional (1D) model, two-dimensional (2D) model, and three-dimensional (3D) model are established to evaluate the performance and stability of the seat’s suspension systems under different operating conditions. The root mean square (RMS) acceleration and power spectral density (PSD) acceleration of the seat have been selected as the evaluation indexes. The mathematical model and numerical simulation method are then tested via the experiment to enhance the reliability of the research results. The research result shows that the seat’s vibration characteristic using 1D, 2D, and 3D models is the same. However, the seat’s RMS acceleration and maximum PSD acceleration using the 1D model are increased by 30.6% and 61.7% in comparison with the 3D model, whereas the seat’s acceleration and PSD acceleration using the 3D model are like the measured results. Thus, the use of the vehicle model greatly influences the research result. By adding the QZSS into the seat’s SASS, the seat’s RMS and maximum PSD accelerations are greatly reduced in comparison with all seat’s PSS, seat’s SASS without the QZSS, and seat’s PSS added by QZSS. Therefore, the seat’s SASS added by the QZSS should be applied to further enhance the vibratory roller’s comfort.

Fault Injection Method and Ground-truth Development to Enable a Low-cost Bearing Fault Monitoring System in the Automotive Industry

Bearing condition monitoring is a widely studied field, but applications to the automotive industry have received little attention as the bearing failure rates are typically low in traditional internal combustion engine vehicles with 200 – 300k mile lifespans. The rapid advancement of electric and autonomous vehicles enables vehicles with million-mile lifespans. This implies that the reliable life of existing bearing designs is exceeded throughout the vehicle life, which can potentially lead to vehicle failure. To enable the development of a bearing fault detection and prognostics system, healthy and faulty bearing data must be collected, and the ground-truth states of the health of bearings need to be determined for algorithm refinement and validation. This work explores the fault injecting options, and ground-truthing together with their limitations. Two methods based on precision machining and seeded spalling are developed and used to inject inner race faults in a ball bearing. A non-invasive ground-truthing method is proposed to quantify the state of health of the fault injected bearings in which bench test data is collected under various speed and load conditions. The vibration signals from the bench tests are used to calculate the root-square of the area under the acceleration Power Spectral Density curve (known as GRMS) for each speed and load condition. To remove the dependency of the results on load and speed conditions, a speed-load-GRMS plot is generated, and a plane is fitted to the data for each fault level. Next, the volume under the plot is calculated, yielding a single cumulative GRMS value for each fault level. This value is used as the ground-truth health of bearing for each fault level. For the bearing with the faults injected using precision machining fault injection, the obtained ground-truth values are 1.56, 3.68, and 4.36 times larger than the same figure for the healthy bearing for the faults with the widths of 0.1 mm, 0.5 mm, and 2 mm, respectively. The observed correlation between the fault sizes and the calculated ground-truth values validates the proposed method which can provide a good separation among different health states of a bearing.

Development of transportation loading spectra for building modules based on a vehicle-module interaction model

The wastage associated with the damage of single building modules when subjected to dynamic loading (termed transportation loading) from heavy vehicles during road transportation is a primary deterrent to the adoption of modular construction. In this paper, generalized transportation loading spectra were developed to quantify transportation loading for the structural design of building modules. First, a shaking table test was conducted on a scaled-down model representing the module transportation scenario to explore the resonant responses between the vehicle and module. Then, a proposed vehicle-module interaction model accurately simulated the vertical acceleration responses derived from the shaking table test. Finally, the vehicle-module interaction model was extended to a realistic module transportation situation; the acceleration power spectral densities (PSDs) on the vehicle chassis from the extended models characterized the loading spectra. A parametric study involving vehicle type, module category, road roughness, and travel speed demonstrates that the loading spectra consist of five scalable PSDs under Class A-E roads (from A-H classification of ISO 8608). Three peaks are observed in each PSD, with two high peaks consistent with measured PSDs from the literature. Among the spectra, PSDs under B-D roads are applicable for most module transportation scenarios.

Random vibration study of functionally graded porous curved beams with elastically restrained ends

Firstly, the random vibration characteristics of functionally graded porous (FGP) curved beams with elastically restrained ends are studied. An efficient model is presented by the Timoshenko beam theory and spectral-Chebyshev method. In this paper, three different types of porous distribution are considered, and the relationship between porosity coefficient and material parameters is determined according to the typical mechanical properties of open cell foam metal. Four types of curved beams with different curvatures are selected for the study, which are elliptical beam, parabolic beam, hyperbolic beam and circular beam. The one-dimensional admissible displacement functions of the FGP curved beam are constructed by Chebyshev polynomials of the first kind with Gauss-Lobatto sampling points discretization. Three artificial boundary springs are used to impose elastic boundary constraints at the ends of the curved beam. The pseudo excitation method is used to apply stationary and non-stationary random excitations, including point excitation and base acceleration excitation. The stationary random vibration responses of the FGP curved beam with different boundary conditions, involving the power spectral density (PSD) and root mean square (RMS) values of displacement, velocity and acceleration, are calculated and agreed well with the finite element method (FEM). At last, the RMS values of the non-stationary random vibration response of the FGP curved beam are given.

A study on an integrated aero-vibro-acoustic analysis procedure for a small-scale supersonic jet and surrounding thin plates

The goal of this paper is to examine the computational approaches for predicting both of the overall sound pressure level (OASPL) at a few locations and acceleration power spectral density (APSD) of surrounding thin plates due to the aero-acoustic pressure generated by a cold jet with M = 1.8. First, computational fluid dynamics (CFD), particularly delayed detached eddy simulation, are applied to predict the OASPL at the near-field and compute the acoustic properties. Second, the linearized boundary element method (BEM), that is, the Helmholtz-Kirchhoff method is utilized to propagate the pressure and obtain the OASPL at the far-field. Finally, the finite element method is implemented to predict the APSD for a clamped thin plate based on the optimal triangle membrane element, discrete Kirchhoff triangle plate bending element, and Newmark- β time integration scheme. Using the present CFD and BEM, the OASPLs are compared with the experimental results measured by microphones at both the near- and far-fields, respectively. Moreover, APSDs are compared with the experimental results obtained by an accelerometer at a few different locations. Although OASPLs are overestimated because of the coarse meshes in the higher-angle area and low order scheme of the present CFD analysis, the present integrated aero-vibro-acoustic analysis is capable of predicting the OASPL and APSD generated by a cold jet with M = 1.8.

Effect of tuned mass damper in wind‐induced response of “V” plan‐shaped tall building

SummaryIn this study, a “V” plan‐shaped building with single tuned mass damper (STMD) and multiple tuned mass damper (MTMD) is analyzed in alongwind and crosswind direction considering different mass ratios and tunning ratios. The force coefficient of the “V” plan‐shaped tall building is determined by computational fluid dynamics (CFD) method to obtain the time history function of dynamic wind force. An optimum ratio has been adopted to compare the effectiveness of MTMD over STMD installed in the V‐shape building model. Power spectral density of displacement, acceleration, base shear, base moment, and torsional moment due to dynamic wind time history are determined to investigate the vibration control of MTMDs and STMDs. Finally, the optimal mass ratio of the maximum reduction in response and control effectiveness in percentage has been determined for each parameter. The present study indicates that MTMDs are more effective to mitigate wind‐induced vibration than STMDs.

Dynamic Response of a Hypersonic Rocket Sled Considering Friction and Wear

The dynamic response of a hypersonic rocket sled was studied by considering the time-varying friction coefficient and the gap caused by wear between the slipper and track. A multibody dynamic model for a hypersonic rocket sled system was established by considering the time-varying mass and moment of inertia, nonlinear aerodynamic loads, engine thrust, track irregularity, and nonlinear contact force. As for the wear calculation, the ductile and shear criteria were used as the material damage criteria, and slipper wear was determined by the number of damaged elements. A rocket sled test was also carried out, and the dynamic response of the sled was measured. The results showed that the computational sliding displacement and velocity of the third-stage sled matched well with the test values. The computational root mean square (RMS) values of the vertical acceleration of the third-stage sled front slipper considering friction and wear matched better with the test values than with the case without considering friction and wear, which underestimated the RMS value by approximately 20.1% at Mach 5. The importance of considering friction and wear and the correctness of the computational method were validated. It is also found that the kinetic friction coefficient decreased with an increase in the product of the pressure and velocity. The wear height of the slipper increased almost linearly with the sliding displacement. The test results showed that the vertical acceleration power spectral density of the third-stage sled front slipper increased with time in the full frequency band below 2000 Hz. This study will guide the design and optimization of hypersonic rocket sleds.

Fatigue Life Analysis of Aluminum Alloy Notched Specimens under Non-Gaussian Excitation based on Fatigue Damage Spectrum

In this study, a non-Gaussian excitation acceleration method is proposed, using aluminum alloy notched specimens as a research object and measured acceleration signal of a certain airborne bracket, during aircraft flight as input excitations, based on the fatigue damage spectrum (FDS) theory. The kurtosis and skewness of the input signal are calculated and the non-Gaussian characteristics and amplitude distribution are evaluated. Five task segments obey a non-Gaussian distribution, while one task segment obeys a Gaussian distribution. The fatigue damage spectrum calculation method of non-Gaussian excitation is derived. The appropriate FDS calculation method is selected for each task segment and the acceleration parameters are set to construct the acceleration power spectral density, which is equivalent to the pseudo-acceleration damage. A finite-element model is established, the notch stress concentration factor of the specimen is calculated, the large mass point method is used to simulate the shaking table excitation, and a random vibration analysis is carried out to calculate the accelerated fatigue life. The simulation results show that the relative error between the original cumulative damage and test original fatigue life is 15.7%. The shaking table test results show that the relative error of fatigue life before and after acceleration is less than 16.95%, and the relative error of test and simulation is 24.27%. The failure time of the specimen is accelerated from approximately 12 h to 1 h, the acceleration ratio reaches 12, and the average acceleration ideal factor is 1.125, which verifies the effectiveness of the acceleration method. It provides a reference for the compilation of the load spectrum and vibration endurance acceleration test of other airborne aircraft equipment.

Influence of Bending Vibration on the Vertical Vibration Behaviour of Railway Vehicles Carbody

The topic of reducing structural vibrations in the case of flexible carbodies of railway vehicles has been intensively studied, but it is still an active research topic thanks to the importance of the perspective of improving the ride comfort. However, no study has been identified in the specialty literature to feature the contribution of the vibration structural modes upon the vibration behaviour of the railway vehicle carbody. The structural vibration modes of the flexible carbodies are particularly complex; however, the first vertical bending mode holds great significance in terms of the ride comfort. This paper analyses the influence of the first vertical bending mode on the vibration behaviour in three reference points of the railway vehicle carbody in correlation with the carbody flexibility, the vehicle velocity and the suspension damping. This study relies on comparisons between the results of the numerical simulations obtained for a ‘flexible carbody’ type model of the vehicle and the ones obtained for a ‘rigid carbody’ type model. The first part of this study analyses the characteristics of the vertical vibrations behaviour of the flexible carbody based on the dynamic response of the vehicle and expressed as the acceleration power spectral density. In the second part, the influence of the vertical bending on the vertical vibrations level of the carbody is analysed using the root mean square of the vertical acceleration.

Optimization analysis of dynamic characteristics of a certain car seat with rigid-flexible coupling

Aiming at the problem of the dynamic comfort of a certain car driver’s seat, from the aspect of selecting the dynamic parameters of the seat cushion, a simulation idea for studying the dynamic comfort of the seat has been proposed. The rigid-flexible coupling dynamics model of the human body and the seat is established through the flexible processing of the seat cushion. ADAMS has been used to analyze the dynamics of the model and compare the changes in the human comfort level when the dynamic parameters of the seat cushion are changed. The optimal range for selecting its dynamic parameters has been obtained. ADAMS/Car has been used to establish a virtual model of the vehicle system, and the dynamic comfort of the model has been analyzed to obtain the human body acceleration power spectral density curve. The results indicate that the optimal selection ranges for seat cushion stiffness and damping are 14∼20N/mm and 0.3∼0.6Ns/mm, respectively. In this range, the resonance frequency of the car seat is lower than the most sensitive frequency of the human body. Use the human comfort evaluation method to verify that the result is reliable, it provides a direction for the subsequent design.

Fatigue Life of Welded Structures under Random Load Study on Frequency Domain Method

In this paper, based on the finite element software, the residual stress of the structure weld is obtained through simulation analysis. The influence of stress concentration is considered by using the mean square stress concentration factor; and the S-N curve equation of the structure is derived. then, the stress power spectrum density of dangerous parts is obtained by random response analysis; Then, the vibration mode of the welded structure is obtained by random response analysis, and the acceleration power spectral density of the structure is input, and then the stress power spectrum density of the dangerous part is obtained Finally, the appropriate stress probability density distribution model is selected to predict the fatigue life with S-N curve equation and Miner damage accumulation theory. The results show that the fatigue life predicted by this method is very close to that of rain flow counting method.

Effect of the Anti-Yaw Damper on Carbody Vertical Vibration and Ride Comfort of Railway Vehicle

The theoretical research on means to reduce the vertical vibrations and improve the ride comfort of the railway vehicle relies on a mechanical model obtained from the simplified representation of the vehicle, while considering the important factors and elements affecting the vibration behaviour of the carbody. One of these elements is the anti-yaw damper, mounted longitudinally, between the bogie and the vehicle carbody. The anti-yaw damper reduces the lateral vibrations and inhibits the yaw motion of the vehicle, a reason for which this element is not usually introduced in the vehicle model when studying the vertical vibrations. Nevertheless, due to the position of the clamping points of the anti-yaw damper onto the carbody and the bogie, the damping force is generated not only in the yawing direction but also in the vertical and longitudinal directions. These forces act upon the vehicle carbody, impacting its vertical vibration behaviour. The paper analyzes the effect of the anti-winding damper on the vertical vibrations of the railway vehicle carbody and the ride comfort, based on the results derived from the numerical simulations. They highlight the influence of the damping, stiffness and the damper mounting angle on the power spectral density of the carbody vertical acceleration and the ride comfort index.

Hardware in the Loop Testing of Adaptive Inertia Weight PSO-Tuned LQR Applied to Vehicle Suspension Control

This paper presents an adaptive inertia weight particle swarm optimization (AIWPSO) employed for solving the multiobjective weight optimization problem of LQR applied for the vehicle active suspension system (ASS). To meet the competing control objectives of ASS including the ride comfort, road handling, and suspension travel, the state feedback controller design for ASS is formulated as an optimization problem and an improved PSO is employed for finding the optimal weights of the linear-quadratic regulator (LQR). Specifically, for solving the premature convergence of the particles and imbalance between exploration and exploitation capabilities of PSO, an adaptive inertia weight that updates the velocity of the particles based on the success rate is used. The efficacy of the AIWPSO-tuned LQR is experimentally tested on a quarter-car ASS plant using the hardware in loop (HIL) testing for an uneven road surface. Experimental results highlight that, compared to conventional PSO-tuned LQR, the proposed scheme can significantly minimize the vehicle body acceleration due to irregular road profile while guaranteeing the minimum tire friction for passenger safety. The ISO 2361-1 standards adopted to evaluate the ride and health criteria substantiate that the proposed scheme reduces the vibration dose value by 25.34% for a bumpy road profile. Moreover, the cumulative power spectral density (CPSD) of vehicle body acceleration assessed in both low- and high-frequency regions manifests the significant improvement in the ride comfort.

Effect of the asymmetry of suspension damping on the ride comfort of railway vehicles

ABSTRACT In terms of reliability, the damper represents the critical element of the suspension in the rail vehicle. A damper failure brings about a reduction in the damping of the suspension it belongs to, thus leading to the asymmetry of the suspension damping in the vehicle. The paper presents an analysis of the effect that the asymmetry of the secondary suspension damping has on the vertical vibration behaviour in the vehicle carbody and on the ride comfort, while using to that purpose the results derived from numerical simulations. The characteristics of the vibration behaviour for the resonance frequencies of the carbody dominant vertical modes are pointed out via the power spectral density of the carbody acceleration, which is weighted by the function of the sensitivity of the human body to the vertical vibrations. The ride comfort is assessed based on the ride index comfort calculated in three carbody reference points – at the centre and above the two bogies.

Low-Cost Reconstruction of Typical Driving Cycles Based on Empirical Information and Low-Frequency Speed Data

A representative driving cycle is crucial to estimating emissions and energy consumptions of vehicles. However, their traditional data acquisition is subject to large sampling requirements and high costs, whether a chase-car method or an on-board measurement method is adopted. Presently, the public transportation department and many private companies collect low-frequency driving data to track and monitor their vehicles. And a large number of typical driving cycles have been generated in the automobile field, which have been limited by the traditional designed method and have not been fully utilized. Herein, we investigate a driving cycle reconstruction method based on empirical information and low-frequency driving data. First, characteristic parameters were selected, based on the ergodicity of a Markov Chain method and an interpolation analysis of the low-frequency data. Second, similar driving cycles were grouped by K-means clustering and principal component analysis, based on the existing typical driving cycles. These were considered as empirical information of the original transient driving cycles. Ultimately, a Markov Chain evolution method based on the empirical information was used to reconstruct driving cycles. The method reconstructs driving cycles using low-frequency data of different sampling intervals, keeping the relative deviations of the characteristic parameters within a threshold range. In comparison with the original driving cycles having a 1-s sampling interval, the reconstructed cycles exhibit a high similarity with the original driving cycles in terms of their velocity and acceleration probability distribution and power spectral density. Additionally, calculation deviation of fuel consumption per 100 km is small. Therefore, this method can estimate energy consumption of urban vehicles in a timely and effective manner.