Statistical modelling of predicted non‐stationary vehicle vibrations

This paper describes a method to predict the vertical vibrations of road vehicles from measured pavement profiles. It discusses the limitations of current methods used for analysing and simulating vehicle vibrations and shows that more accurate characterization and simulation of the transport environment must take into account the non‐stationary nature of road vehicle vibrations. Vertical vibrations for typical transport vehicles under various operating conditions and pavement profiles are predicted using a computer model of the vehicle characteristics and analysed to produce the spectral and statistical characteristics. The paper also presents an improved method to compute the vibration intensity by using a dynamic segmentation data reduction technique. The effectiveness of the procedure to characterize the non‐stationarity of random vehicle vibrations is demonstrated. Finally, the paper deals with the statistical distribution of the vibration intensity and demonstrates how it can be adapted to a technique for the simulation the non‐stationary nature of random vehicle vibrations. Copyright © 2002 John Wiley & Sons, Ltd.     

Using the Weibull distribution to characterise road transport vibration levels

This paper reviews the various ways that have been proposed to characterise road transport vehicle vibrations and recommends a new approach to characterise the vibrations levels during a transport journey. Some 47 road vehicle vibration records, obtained from a broad range of conditions, were analysed, and results show that the root-mean-square (rms) distribution of the vibrations can be accurately modelled with a reduced version of the three-parameter Weibull distribution (shape parameter set to 2). This statistical approach to characterising road vehicle vibrations takes into account the random fluctuations in rms levels that occur naturally during a road journey and can be used to classify the severity of RVV. This offers significant improvement on the simplistic mean rms value that has, so far, been the sole parameter to describe vibration levels during transport. The Weibull location parameter represents the low threshold of the rms level in the record (except when xo is less than zero, in which case the low rms threshold is zero), whereas the Weibull range parameter is proportional to the range of rms level. Results also reveal a strong relationship between the rms mean and the sum of the location and scale parameters. In addition, this enables generation of rms distributions from the mean power density spectrum (PDS) alone. The modified (fixed-shape) Weibull distribution can be used to faithfully describe the entire statistical distribution of the rms level of a journey or transport mode with just two parameters. This new approach can be used in a practical way for quantifying and comparing transport vibration rms levels for design and testing purposes.     

On the time compression (test acceleration) of broadband random vibration tests

Many broadband random vibration tests are time compressed. This is done by increasing test intensity according to the Basquin model of cyclic fatigue. Conventionally, the test level is accelerated from the root mean acceleration and an assumed power constant (k = 2) is applied. Using conventional analysis the potential error in test severity can be very large if k is incorrect. The Miner–Palmgren hypothesis of accumulated fatigue is used to re‐assess the potential error in test severity accounting for the non‐stationarity found in road distribution. This shows a substantially reduced sensitivity to the value of k depending on the distribution of actual vibration intensities around the time‐compressed test intensity. Using an example of a leaf‐sprung vehicle, the conventional level of time compression is shown to have low sensitivity to errors in k, whereas for an example of an air‐ride vehicle a lower level of time compression is needed to reduce error sensitivity. Copyright © 2010 John Wiley & Sons, Ltd.     

Synthesizing nonstationary,non‐Gaussian random vibrations

This paper presents a novel technique by which non‐Gaussian vibrations are synthesized by generating a sequence of random Gaussian processes of varying root mean square (rms) levels and durations. The technique makes use of previous research by the authors which shows that non‐Gaussian vibrations can be decomposed into a sequence of Gaussian processes. Synthesis is achieved by first computing a modulation function which is produced from the rms and the segment length distribution functions, both of which were developed in previous research. This is achieved by first generating a sequence of uniformly distributed random numbers scaled to the range of segment length, which itself is a function of the desired total duration of the synthesized process. In order to transform a uniformly distributed random variable into any arbitrary non‐uniform distribution, the cumulative distribution function is established and used as a transfer function applied to the uniformly distributed random variable. This modulation function is applied to a Gaussian random signal itself generated by a standard laboratory random vibration controller (RVC) by means of a purposed‐designed variable gain amplifier system. In order to counteract the feedback function of the RVC, a second variable gain amplifier is introduced into the system in order to attenuate the feedback signal in inverse proportion to the gain applied to the command signal. This result is a nonstationary, non‐Gaussian random signal that statistically conforms to the desired PSD as well as the RMS distribution function. Copyright © 2010 John Wiley & Sons, Ltd.     

Monitoring and simulating non‐stationary vibrations for package optimization

This paper introduces a new method to analyse and simulate vibrations of transport vehicles. The method pays particular attention to the non‐stationary nature of vibrations, especially during road transport. The limitations of current methods used for analysing and simulating vehicle vibrations are demonstrated. The paper shows how the Hilbert transform can be used to compute the vibration intensity and offers substantial data reduction advantages. It is shown how statistical characteristics of the vibration intensity can be combined with spectral characteristics to enable more realistic simulations of transport vibrations. Finally, it is shown how the processed data is well suited for use with modern telemetry techniques integrated with web browser technologies. Copyright © 2000 John Wiley & Sons, Ltd.     

Review Paper on Road Vehicle Vibration Simulation for Packaging Testing Purposes

Inefficient packaging constitutes a global problem that costs hundreds of billions of dollars, not to mention the additional environmental impacts. An insufficient level of packaging increases the occurrence of product damage, while an excessive level increases the packages' weight and volume, thereby increasing distribution cost. This problem is well known, and for many years, engineers have tried to optimize packaging to protect products from transport hazards for minimum cost. Road vehicle shocks and vibrations, which is one of the primary causes of damage, need to be accurately simulated to achieve optimized product protection. Over the past 50 years, road vehicle vibration physical simulation has progressed significantly from simple mechanical machines to sophisticated computer‐driven shaking tables. There now exists a broad variety of different methods used for transport simulation. Each of them addresses different particularities of the road vehicle vibration. Because of the nature of the road and vehicles, different sources and processes are present in the vibration affecting freight. Those processes can be simplified as the vibration generated by the general road surface unevenness, road surface aberrations (cracks, bumps, potholes, etc.) and the vehicle drivetrain system (wheels, drivetrain, engine, etc.). A review of the transport vibration simulation methods is required to identify and critically evaluate the recent developments. This review begins with an overview of the standardized methods followed by the more advanced developments that focus on the different random processes of vehicle vibration by simulating non‐Gaussian, non‐stationary, transient and harmonic signals. As no ideal method exists yet, the review presented in this paper is a guide for further research and development on the topic. Copyright © 2015 John Wiley & Sons, Ltd.     

A New Approach for Road‐Vehicle Vibration Simulation

A new approach for road‐vehicle vibration simulation is proposed and demonstrated feasible by testing with three express‐road vehicle‐vibration records, that is, record A, two‐wheel electric bicycle, 80% loaded, traveling on urban road; record B, median van, 50% loaded, traveling on urban road; and record C, minivan, 80% loaded, traveling on urban road too. This method decomposes the original signal into a series of approximate Gaussian‐vibration segments and a shock segment with high kurtosis by moving crest factor and one‐tenth peak‐value method. Simulate Gaussian‐distribution vibration one by one from the power spectral density (PSD) of each decomposed segments. The overall signal is simulated by concatenating of each decomposed Gaussian segment. The simulated signal has not only the same overall root‐mean‐square (RMS), duration as the original signal, but also has a similar PSD to the original signal, without incurring excessive acceleration levels. This allows an improved and more representative simulated input signal to be generated that can be use in the current generation of vibration table.     

Characterising heave,pitch, and roll motion of road vehicles with principal component and frequency analysis

For the great majority of transport vehicles, the magnitude of the heave vibration is generally more severe than pitch and roll. Consequently, the measurement, analysis, and simulation of the vehicle vibrations have been focused on vertical vibration. Despite this, it is now being increasingly recognised that the combination of heave, pitch, and roll vibratory motion can induce more severe damage to shipments than vertical vibration alone. Although the pitch and roll motion of road vehicles can now be readily measured, there is little information on how to analyse the data to produce meaningful statistical relationships between the three variables. This paper builds upon previous work that showed that there is some correlation between pitch, roll, and heave motion and that these relationships are dependent on vehicle geometry, including payload mass, centre of mass, vehicle roll centre, and moments of inertia as well as vehicle speed and the road surface. In this paper, data from a range of quasi‐controlled experiments, which involved driving vehicles at constant‐speed on selected roads, were analysed using principal component analysis as well as frequency domain analysis to reveal the relationship between heave, pitch, and roll motion. This was undertaken for a variety of vehicle speeds and routes in order to establish if they influence pitch and roll response. Results are presented in the form of distribution functions, statistical coefficients, and frequency response functions, all of which are useful for helping to define parameters for the simulation of complete, three‐axis vibrations using multi‐axis vibration test systems.     

On the Use of Machine Learning to Detect Shocks in Road Vehicle Vibration Signals

The characterization of transportation hazards is paramount for protective packaging validation. It is used to estimate and simulate the loads and stresses occurring during transport that are essential to optimize packaging and ensure that products will resist the transportation environment with the minimum amount of protective material. Characterizing road transportation vibrations is rather complex because of the nature of the dynamic motion produced by vehicles. For instance, different levels of vibration are induced to freight depending on the vehicle speed and the road surface; which often results in non‐stationary random vibration. Road aberrations (such as cracks, potholes and speed bumps) also produce transient vibrations (shocks) that can damage products. Because shocks and random vibrations cannot be analysed with the same statistical tools, the shocks have to be separated from the underlying vibrations. Both of these dynamic loads have to be characterized separately because they have different damaging effects. This task is challenging because both types of vibration are recorded on a vehicle within the same vibration signal. This paper proposes to use machine learning to identify shocks present in acceleration signals measured on road vehicles. In this paper, a machine learning algorithm is trained to identify shocks buried within road vehicle vibration signals. These signals are artificially generated using non‐stationary random vibration and shock impulses that reproduce typical vehicle dynamic behaviour. The results show that the machine learning algorithm is considerably more accurate and reliable in identifying shocks than the more common approaches based on the crest factor. Copyright © 2016 John Wiley & Sons, Ltd.     

Some characteristics of the heave,pitch and roll vibrations within urban delivery routes

Until recently, laboratory testing of packaged systems has been undertaken by simulating vertical vibrations alone. However, with increasing demand for a reduction in packaging waste, the use lightweight systems, such as stretch film, is increasing. Such containment systems are susceptible to the lateral forces generated by the pitch and roll vibratory motion of vehicles due to road surface unevenness. If laboratory simulation is to be realistic, multi-axial motion must be taken into account and an understanding of the relationships between the random heave, pitch, and roll vibrations is essential. This paper uses vibration data collected from a number of transport vehicles traveling along typical urban and suburban routes to establish the nature and level of the multi-axial vibrations that exist. These are presented with average Power Density Spectra (PDS) as well as statistical distributions of the moving root-mean-square (rms). The paper analyses the data for correlation of the rms levels with respect to nonstationarity. This is important when simulating nonstationary (randomly fluctuating rms) vibrations for heave, pitch and roll. These statistical correlation functions are used to manage the relative rms levels of each of the three Degrees of Freedom (DoFs) when undertaking vibration simulations using multi-axis vibration test systems. The results show that the relationships between the moving rms of heave, pitch and roll vibrations are not strongly correlated but can be characterized statistically as joint distributions to enable realistic simulation of multi-axial random vibrations of road transport vehicles under controlled laboratory conditions .     

A hierarchical finite element for geometrically non‐linear vibration of doubly curved,moderately thick isotropic shallow shells

A p‐version, hierarchical finite element for doubly curved, moderately thick, isotropic shallow shells is derived and geometrically non‐linear free vibrations of panels with rectangular planform are investigated. The geometrical non‐linearity is due to large displacements, and the effects of the rotatory inertia and transverse shear are considered. The time domain equations of motion are obtained by applying the principle of virtual work and the d'Alembert's principle. These equations are mapped to the frequency domain by the harmonic balance method, and are finally solved by a predictor–corrector method. The convergence properties of the element proposed and the influence of several parameters on the dynamic response are studied. These parameters are the shell's thickness, the width‐to‐length ratio, the curvature‐to‐width ratio and the ratio between curvature radii. The first and higher order modes are analysed. Some results are compared with results published or calculated using a commercial finite element package. It is demonstrated that with the proposed element low‐dimensional, accurate models are obtained. Copyright © 2002 John Wiley & Sons, Ltd.     

Flow induced vibrations of a triangular tube array in various arrangements of orientation and natural frequency

Abstract

Crossflow induced vibrations of a triangular tube array with a pitch ratio 1.33 were investigated experimentally. The streamwise and cross‐stream displacements of a monitored tube in the array were simultaneously measured by two accelerometers to examine the tube response to the cross flow in a water tunnel. The experiment was aimed to study the effects of the array orientation, and the tube's natural frequency on the flow induced vibration of the tube array. It is shown by amplitude diagrams that fluid elastic vibrations exist when the reduced velocity is above a critical value. The critical reduced velocity is found to be sensitive to the orientation of the test array. Based on the measured data of critical reduced velocity, the tube array in a triangular pattern (at a 30‐deg orientation with respect to the flow direction in the experiment) is found to be more stable than when in a rotated triangular pattern (0‐deg orientation). Furthermore, it is illustrated that the discrepancy in natural frequency of the tubes delays the occurrence of the fluid elastic vibrations of the tube array. With all the tubes in the test array having the same natural frequency, the orbits of the tube that exhibits fluid elastic vibrations are an organized, elliptic shape. The corresponding spectra are line‐dominated with peaks at the natural frequency and its harmonics, suggesting that the tube vibration is an organized oscillator. Without the same natural frequency as the surrounding tubes, the monitored tube exhibits fluid elastic vibration at larger reduced velocity, vibrating in a relatively random orbit.     

EWMA Control Chart Performance with Estimated Parameters under Non‐normality

Exponentially weighted moving average (EWMA) control charts can be designed to detect shifts in the underlying process parameters quickly while enjoying robustness to non‐normality. Past studies have shown that performance of various EWMA control charts can be adversely affected when parameters are estimated or observations do not follow a normal distribution. To the best of our knowledge, simultaneous effect of parameter estimation and non‐normality has not been studied so far. In this paper, a Markov chain approach is used to model and evaluate performance of EWMA control charts when parameter estimation is subject to non‐normality using skewed and heavy‐tailed symmetric distributions. Using standard deviation of the run length (SDRL), average run length (ARL), and percentiles of run lengths for various phase I sample sizes, we show that larger phase I sample sizes do not necessarily lead to a better performance for non‐normal observations. Copyright © 2015 John Wiley & Sons, Ltd.     

A p‐version,first order shear deformation,finite element for geometrically non‐linear vibration of curved beams

A p‐version, hierarchical finite element for curved, moderately thick, elastic and isotropic beams is introduced. The convergence properties of the element are analysed and some results are compared with results published elsewhere or calculated using a commercial finite element package. It is verified that, with the proposed element, shear locking does not affect the computation of the natural frequencies and that low dimensional, accurate models are obtainable. Geometrically non‐linear vibrations due to finite deformations, which occur for harmonic excitations with frequencies close to the first three natural frequencies of vibration, are investigated using Newmark's method. The influence of the thickness, longitudinal inertia and curvature radius on the dynamic behaviour of curved beams are studied. Copyright © 2004 John Wiley & Sons, Ltd.     

Comparison study on simulation effect of improved simulation methods for packaging random vibration test

In general, existing testing methods for packaging design employ Gaussian distributions to represent vibration induced by road profiles. However, the actual road vehicle vibration is non‐Gaussian. The key limitation is that the simulated Gaussian vibration cannot reconstruct the shock events buried in the vibration, which will result in inaccurate reliability evaluation of cushion packaging. A new simulation technique called shock extraction has been proposed and validated in our earlier study. This article is a further study of our previous research. The shock extraction method has been compared with other three representative simulation methods including the single‐level PSD, three‐way split spectral, and wavelet decomposition in terms of simulation effect. Signal simulated by the shock extraction method possesses the same vibration intensity, duration, approximate statistical characteristics, and PSD plots with the original signal. The results show that the simulation effect of the shock extraction method is the best, and the worst is the single‐level PSD. The wavelet decomposition and three‐way split spectral are somewhere in the middle.     

基于典型路况车身加速度提取及其影响因素分析

通过搭建载荷谱测试采集系统,按试验规范采集了4台不同载荷的试验车载荷谱,并准确提取多种强化路面的车身加速度信号。由此在时域内计算各试验车在多种强化路上的加速度均方根,得到强化路与普通路均方根的相对值。根据车轮-车身双质量振动模型分析汽车行驶速度、路面、车身载荷对车身加速度均方根值的影响,结合实际采集数据进行统计分析。结果表明,加速度均方根和相对值受强化路面影响较大,在一定的范围内取值,并与车速约成0.009线性相关,与载荷负相关,随载荷的增加变小,低载时变化不明显,载荷增加趋势明显。这一结论可为汽车性能评价和使用载荷的选取提供依据。     

EWMA Dispersion Control Charts for Normal and Non‐normal Processes

Process monitoring through control charts is a quite popular practice in statistical process control. This study is planned for monitoring the process dispersion parameter using exponentially weighted moving average (EWMA) control chart scheme. Most of the EWMA dispersion charts that have been proposed are based on the assumption that the parent distribution of the quality characteristic is normal, which is not always the case. In this study, we develop new EWMA charts based on a wide range of dispersion estimates for processes following normal and non‐normal parent distributions. The performance of all the charts is evaluated and compared using run length characteristics (such as the average run length). Extra quadratic loss, relative average run length, and performance comparison index measures are also used to examine the overall effectiveness of the EWMA dispersion charts.Copyright © 2014 John Wiley & Sons, Ltd.     

Creating Transport Vibration Simulation Profiles from Vehicle and Road Characteristics

It is today generally accepted that to carry‐out realistic transport simulation trials, field data must be acquired from vehicles travelling on the actual route(s) to be used for a particular distribution environment. This approach requires time, effort, access to data recording equipment as well as the necessary expertise to analyse the collected data. Often, this is out of reach of smaller operators who want a reasonable approximation without the time and expense. Currently, the only available option is the adoption of generic test spectra and levels that have been shown to be approximate representations of distribution environments. This paper discusses an alternative and practical method that uses some knowledge of the dynamic characteristics of various vehicle types along with an assessment of the types of roads (road roughness) to be encountered along a particular route. The method exploits the fact that the spectral characteristics (power spectral density) of road profiles are well known. The paper shows how this road surface elevation spectral function is combined with a numerical model of a particular vehicle type and speed to produce a target vibration power spectral density suitable for vibration test systems. One added benefit is that the method is capable of calculating the variations in root mean square levels of the response vibrations. This is presented as the root mean square distribution which, when coupled with the target power spectral density, can be used to synthesize realistic random vibrations that bear statistical similitude with real, field vibrations. Copyright © 2012 John Wiley & Sons, Ltd.     

《列车引发建筑物振动试验及数值隔振研究》

首先通过现场测试的方法对铁路线附近建筑物的振动特性、建筑物振动的传播规律及其影响因素进行了研究,然后建立了列车 大地 隔振沟 建筑物耦合动力分析模型,对隔振沟的沟深、沟长、沟到建筑物的距离和填充材料等四种结构参数对隔振效果的影响进行了分析。结果表明：列车引发的建筑物振动属于低频振动,建筑物结构对高频振动具有衰减的作用;振动随列车速度的提升而增大,随列车编组的加长而增大,随列车轴重的增加而增大;建筑物的振动水平随楼层的上升呈曲折分布;隔振沟的沟深、沟长、沟与建筑物之间的距离以及填充材料的变化对建筑物楼板的振动都有比较大的影响。