Evaluation of fractal dimension of soft terrain surface

By using a laser profiler, the roughness of sowed and plowed surfaces was obtained. Through evaluation of the precision of fractal dimensions based on the Weierstrass–Mandelbort (W–M) function, we found the rescaled (R/S) analysis method and the structure spectral method were not suitable for the calculation of the fractal dimension on a soft terrain surface. Therefore, the fractal dimension, non-scale range and correlation coefficient for each kind of terrain were analyzed using the following fractal computational methods – (i) variate-difference method, (ii) power spectral density method, and (iii) root mean square method. The results showed that: fractal dimension of plowed terrain was large with small fluctuations, while its internal structure was complex. The power spectral density method was not robust enough to compute the fractal dimension of a soft terrain surface. The fractal dimension computed using the root mean square method was found to be more accurate for the soft terrain surface. Moreover, the correlation coefficient of linear regression when using the root mean square method was good and the range of non-scale variation was small.     

Fractal characteristics of rocks fractured under tension

Fractal geometry can be useful for explaining the fracture behavior and rock properties. The fractal properties of rock fracture surface developed under tension were examined. Seven different rock samples were selected for the tests. An automated surface scanning device was used to map the fractured surfaces. Variogram analysis (VA) (for 1D self-affine sets) and power spectral density (PSD) measurement (for 2D self-affine sets) were applied to calculate the fractal dimension. On a comparative basis, there exists a trend between the fractal dimension and loading rate. The profiles in the loading direction yield higher fractal dimensions indicating the anisotropic feature of fractal. The fractal dimensions obtained by PSD and VA display a relationship for grain size and porosity. Higher porosity samples give different fractal dimensions for upper and lower fractures surfaces.     

Fractal Prediction Model of Spontaneous Imbibition Rate

By utilizing fractal dimension as one of the parameters to characterize rocks, a mathematical model was derived to predict the production rate by spontaneous imbibition. This fractal production model predicts a power law relationship between spontaneous imbibition rate and time. Fractal dimension can be estimated from the fractal production model using the experimental data of spontaneous imbibition in porous media. The experimental data of recovery in gas-water-rock and oil–water–rock systems were used to test the fractal production model. The rocks (Berea sandstone, chalk, and The Geysers graywacke) in which the spontaneous water imbibition experiments were conducted had different permeabilities ranging from 0.5 to over 1000 md. The results demonstrate that the fractal production model can match the experimental data satisfactorily in the cases studied. The fractal dimension data inferred from the model match were approximately equal to the values of fractal dimension measured using a different technique (mercury-intrusion capillary pressure) in Berea sandstone.     

Calculating fractal parameters from low-resolution terrain profiles

Driver comfort on rough terrain is an important factor in the off-road performance of wheeled and tracked ground vehicles. The roughness of a terrain has typically been quantified by the U.S. Army as the root-mean-square elevation deviation (RMS) of the terrain profile. Although RMS is an important input into many mobility calculations, it is not scale invariant, making it difficult to estimate RMS from low resolution terrain profiles. Fractal parameters are another measure of roughness that are scale invariant, making them a convenient proxy for RMS. While previous work found an empirical relationship between fractal dimension and RMS, this work will show that, by including the cutoff length, an analytic relationship between fractal properties and RMS can be employed. The relationship has no free parameters and agrees very well with experimental data - thus providing a powerful predictive tool for future analyses and a reliable way to calculate surface roughness from low-resolution terrain data in a way that is scale invariant. In addition, we show that this method applies to both man-made ride courses and natural terrain profiles.     

基于逆虚拟激励法的垂向轨道不平顺功率谱识别

提出一种识别轨道垂向不平顺功率谱的新方法.采用定点激励的垂向车辆-板式轨道耦合动力学模型.车辆简化为多刚体模型,板式轨道考虑为3层梁模型,并通过线性轮轨力耦合车辆模型和轨道模型.以轴箱加速度作为测量对象,采用逆虚拟激励法识别垂向轨道不平顺的功率谱,并研究了测量误差和车辆运行速度对垂向轨道不平顺的识别精度的影响.数值结果表明,本文方法能够较为准确地识别垂向轨道不平顺功率谱,为列车运行环境载荷识别与评估提供了新的途径.     

Assessment of tracked vehicle suspension system using a validated computer simulation model

A non-linear, in-plane computer simulation model of a typical high-mobility tracked vehicle is developed for suspension dynamic analysis and ride quality assessment. The Langrangian model formulation of the tracked vehicle is derived considering an arbitrary rigid terrain profile and constant vehicle speed. The model incorporates detailed representations of a trailing arm suspension system and dynamic wheel-track-terrain interactions. The computer model predictions are validated against field measurements, which were gathered from tests of an armoured personnel carrier traversing a discrete half-round bump and a random course. A parametric sensitivity analysis was carried out using the validated computer model in order to assess the influence of conventional suspension parameters on the ride performance of the test vehicle. In addition, the ride performance potentials of an alternate hydrogas suspension configuration were investigated.     

A fractal analysis of subcooled flow boiling heat transfer

A fractal model for the subcooled flow boiling heat transfer is proposed in this paper. The analytical expressions for the subcooled flow boiling heat transfer are derived based on the fractal distribution of nucleation sites on boiling surfaces. The proposed fractal model for the subcooled flow boiling heat transfer is found to be a function of wall superheat, liquid subcooling, bulk velocity of fluid (or Reynolds number), fractal dimension, the minimum and maximum active cavity size, the contact angle and physical properties of fluid. No additional/new empirical constant is introduced, and the proposed model contains less empirical constants than the conventional models. The proposed model takes into account all the possible mechanisms for subcooled flow boiling heat transfer. The model predictions are compared with the existing experimental data, and fair agreement between the model predictions and experimental data is found for different bulk flow rates.     

Analytical track models for ride dynamic simulation of tracked vehicles

This paper presents various modelling strategies to account for track in the ride dynamic simulation of high mobility tracked vehicles negotiating rough off-road terrains. Four analytical track representations of varying complexities are formulated in conjuction with an in-plane ride dynamic model of a typical tracked vehicle. These track models are conceived in view of the tracked vehicle kinematics while ignoring the track belt vibrations. The ride dynamic response of a conventional armoured personnel carrier is evaluated in conjunction with different track methods, and validated against field-measured ride data. The relative performances of these track models are thus assessed based on the accuracy of response predictions, and associated computational time.     

A fractal reconstruction method for LDV spectral analysis

An unequally spaced fractal interpolation method is developed to reconstruct the low data rate laser Doppler velocimetry (LDV) signal for better spectral results. The reconstructed result not only augments the data points to improve the statistics but also retains the turbulent fractal dimension of the flow. In other words, the interpolated data are flow turbulence-correlated data which are physically reasonable. This method is demonstrated on the LDV spectral measurements in the shear layer of a jet flow and the results are compared against the hot-wire spectral data. When the data rate of the LDV signal is low, the fractal interpolation method can suitably restore the major spectral peaks while the conventional sample-and-hold fails. Effects of the data rate, data record length, sampling rate and the fractal dimension on the accuracy of the spectral reconstruction are also discussed. A version of this paper was presented at the 4th International Symposium on Transport Phenomena in Heat and Mass Transfer, July 14–18, 1991, Sydney, Australia     

Fractal dimension as a characteristic of deformation stages of austenite stainless steel under tensile load

A technique for defining the fractal dimension of the deformed specimen is considered by using surface relief images obtained from a scanning electron microscope. By subjecting the austenitic stainless steel specimen to a step-wise increase in load, the fractal dimension is observed. Surface mesostructure could be characterized by discrete fractal dimension. The spectrum of the fractal data agrees with the self-affinity function calculated from the universal material constant. A correlation is established between the step-wise increase in the fractal dimension and the specific energies dissipated in the deformed specimen.     

Analysis of fetal cortical complexity from MR images using 3D entropy based information fractal dimension

The fetal cortical complexity is a significant quantification for assessing the development of fetal brain. This study attempts to quantify the development of fetal cortical complexity using the concept of fractal dimension (FD) analysis. Thirty-two fetal MR images were selected from Taipei Veterans General Hospital at 27–37 weeks of gestational age (GA). To investigate the FD of fetal cortical complexity, the entropy based information fractal dimension method (FD _EBI), which is modified from Box-Counting method, was adopted and extended from 2D to 3D. The FD results from overall whole fetal brains show that the increase of cortical complexity is highly correlated with the gestational age of the fetus. Moreover, the FD values of right hemispheric brain are larger than those of left hemispheric brain, show that the development of right hemispheric fetal cortical complexity earlier than the left. These results are in good agreement with normal fetal brain development and suggest that the FD is an effective means for the quantification of fetal cortical complexity.     

Evolutionary algorithm-based PID controller tuning for nonlinear quarter-car electrohydraulic vehicle suspensions

The basic challenge associated with the design of vehicle suspension system is the attainment of an optimal trade-off between the various design objectives. This study presents the design of proportional-integral-derivative (PID) controller for a quarter-car active vehicle suspension system (AVSS) using evolutionary algorithms (EA) such as the particle swarm optimization (PSO), genetic algorithm (GA) and differential evolution (DE). Each of the EA-based PID controllers showed overall improvement in suspension travel, ride comfort, settling time and road holding from the manually tuned controller and the passive vehicle suspension system. These improvements were, however, achieved at the cost of increased actuator force, power consumption and spool-valve displacement. DE-optimized PID control resulted in the best minimized suspension performance, followed by the GA and PSO, respectively. Frequency-domain analysis showed that all the signals were attenuated within the whole body vibration frequency range and the EA-optimized controllers had RMS frequency weighted body acceleration of the vehicle within allowable limits for vibration exposure. Robustness analysis of the DE-optimized PID-controlled AVSS to model uncertainties is carried out in the form of variation in vehicle sprung mass loading, tyre stiffness and speed.     

单轴下岩石声发射参数的分形特征

通过采集大理岩和红砂岩单轴压缩声发射信 号,引入关联分维函数,计算了不同应力水平下的声发射过程时间序列的关联维数,得 到了关联分维数与应力水平的变化关系. 结果表明,在同一应力水平下,随着$m$值的 增大, AE过程的分形特征越不明显;在不同应力水平下,关联分维数不同, AE过程参数具有不同的自相似和分形程度. 同时发现,声发射过程参数的分形特 征具有一定的尺度范围.     

Efficient estimation of power spectral density from laser Doppler anemometer data

 A non-biased estimator of power spectral density (PSD) is introduced for data obtained from a zeroth order interpolated laser Doppler anemometer (LDA) data set. The systematic error, sometimes referred to as the “particle-rate filter” effect, is removed using an FIR filter parameterized using the mean particle rate. Independent from this, a procedure for estimating the measurement system noise is introduced and applied to the estimated spectra. The spectral estimation is performed in the domain of the autocorrelation function and assumes no further process parameters. The new technique is illustrated using simulated and measured data, in the latter case with direct comparison to simultaneously acquired hot-wire data. Received: 9 June 1997/Accepted: 14 October 1997     

Ride comfort evaluation for road vehicle based on rigid-flexible coupling multibody dynamics

In the present research two different whole vehicle multibody models are established respectively, including rigid and rigid-flexible coupling multibody vehicle models. The former is all composed by rigid bodies while in the later model, the flexible rear suspension is built based on the finite element method (FEM) and mode superposition method, in which the deformations of the components are considered. The ride simulations with different speeds are carried out on a 3D digitalized road, and the weighted root mean square (RMS) of accelerations on the seat surface, backrest and at the feet are calculated. The comparison between the responses of the rigid and rigid-flexible coupling multibody models shows that the flexibility of the vehicle parts significantly affects the accelerations at each position, and it is necessary to take the flexibility effects into account for the assessment of ride comfort.     

Application of nonlinear spectral analysis and signal reconstruction to laser Doppler velocimetry

Spectral analysis is a useful tool in engineering applications but many practical problems are encountered in computing power spectral densities (PSD), particularly in laser Doppler velocimetry where data are irregularly sampled. Methods to compute PSD are usely based on discrete Fourier transforms such as FFT. A non linear spectral analysis approach is tested and found to give better results, particularly with short data records. Results are also quite promising when non linear spectral analysis is combined with signal reconstruction to process irregularly sampled data.A preliminary version of this paper has been presented at LDA specialist meeting on the use of computers, May 1987, Institut Saint Louis, France     

基于基底长度的粗糙表面分形接触模型的构建与分析

为建立更为精确的粗糙表面接触模型,根据微凸体变形特征、分形理论以及摩擦的作用,从微观角度基于基底长度建立了粗糙表面分形接触模型.通过与其他粗糙表面接触模型和实验数据的比较,验证了本文模型的正确与合理,并由数值仿真分析了分形维数、接触载荷与真实接触面积之间的相互关系.分析结果表明:特征尺度一定时,要维持一定的真实接触面积,分形维数越大,所需要的力也越大;分形维数与特征尺度一定时,随着载荷的增加,接触面积也在增加;特征尺度与接触力一定时,随着分形维数的增大,真实接触面积在减小.该模型的建立为进一步研究粗糙表面的摩擦、磨损与润滑提供了理论依据.     

复杂高耸结构风振响应研究

本文提出了基于高频动态测力天平试验的风振响应的频域分析方法,采用该方法可以用来求解复杂高耸结构的三维耦联风振响应,并给出了利用高频动态测力天平试验来确定广义模态力谱的计算方法.该方法利用高频动态测力天平试验得到的基底剪力自谱、基底弯矩自谱以及基底剪力与弯矩的互谱与脉动风荷载的自谱密度的相互关系并通过引入振型修正系数来求得广义模态力谱,求解结构的三维耦联风振响应.然后,采用本文方法对在建的河南省广播电视发射塔的风振响应进行了研究,结果表明横风向的位移和加速度响应的均方根值要大于顺风向,因此在计算中必须考虑横风向风振的影响.最后本文对计算振型数目和模态耦联项对结构风振响应的影响进行了分析.本文的方法对于求解复杂高耸结构的风振响应具有重要的借鉴意义.     

Hydro-gas suspension system for a tracked vehicle: Modeling and analysis

Tracked vehicles fitted with torsion bar suspensions are limited in their ability to achieve high mobility. This limitation is due to the linear characteristics and the consequent poorer ride performance. Hydro-gas suspensions due to their inherent non-linear behavior can provide higher mobility and better ride comfort performance. The hydro-gas suspension model has usually been developed from experimental force-displacement characteristics, which requires availability of suspension hardware.In this paper, a hydro-gas suspension system is modeled using polytropic gas compression model to represent the spring characteristics, while the damper orifices are modeled using hydraulic conductance. The analytical model is then validated with experiments individually for spring and damper flow characteristics and then as a suspension-wheel assembly in a test rig. The validated suspension model is incorporated in an in-plane model. Using this model, simulation is carried out for sinusoidal inputs of different wavelengths, amplitudes and vehicle speeds. The simulation model is validated with data measured on a vehicle traversing an APG course. The proposed model agrees very well with the measured data. Based on the validated model, studies on the influence of suspension parameters on the ride comfort of a tracked vehicle are carried out.     

Country road and field surface profiles acquisition,modelling and synthetic realisation for evaluating fatigue life of agricultural machinery

Fatigue life of agricultural machinery is strongly affected by the surfaces that these machines operate on. In the present paper a sensor-frame was developed to acquire road and field profiles in absolute geo-referenced coordinates. The sensor-frame was validated by measuring discrete trapezoidal bumps with known dimensions resulting in a root mean squared (RMS) error of 6–8 mm. Profiles were acquired from a country road and from a mowed grass field. Using the quarter-car vehicle model, the movement of an agricultural vehicle was simulated for various speeds. The resulted vertical loads were rainflow-counted and the accumulated fatigue pseudo damage was calculated using Palmgren–Miner linear rule. Based on the derived Power Spectrum Density (PSD), the profiles were classified according to ISO 8608 standard. Two methodologies were followed to model and create a number of synthetic realisations for each profile: Direct Spectrum Estimate (DSE) and ISO based modelling. Simulating the produced synthetic profiles with the quarter-car vehicle model, the corresponding pseudo damage was calculated. The accumulated damages from the DSE models were closer to the corresponding ones from the measured profiles. ISO based models could not model the profile irregularities, which proved to contribute the largest part of the accumulated fatigue damage.