Estimation and Prediction of the Condition of the Vehicle Engine Based on the Correlation Dimension

This paper applies the fractal dimension as a characteristic to describe the engine抯 operating condition and its developmental trend. A correlation dimension is one of the quantities that are usually used to characterize a strange attractor. With the operation of the phase space reconstruction, respective correlation dimensions of a series of vibration signals obtained under different conditions are calculated to find the intrinsic relationship between the indicator and the operating condition. The experiment result shows that the correlation dimension is sensitive to the condition evolution and convenient for the identification of abnormal operational states. In advanced prognostic algorithm based on the BP neural network is then applied on the correlation dimensions to predict the short-term running conditions in order to avoid severe faults and realize in-time maintenance. Experimental results are presented to illustrate the proposed methodology.

ON A CLASS OF BESICOVITCH FUNCTIONS TO HAVE EXACT BOX DIMENSION: A NECESSARY AND SUFFICIENT CONDITION

This paper summarized recent achievements obtained by the authors about the box dimensions of the Besicovitch functions given bywhere 1 < s < 2, λk> tends to infinity as k→∞ and λk satisfies λk+1/λk≥λ>1. The results show thatis a necessary and sufficient condition for Graph(B(t)) to have same upper and lower box dimensions. For the fractional Riemann-Liouvtlle differential operator Du and the fractional integral operator D-v, the results show that if A is sufficiently large, then a necessary and sufficient condition for box dimensionof Graph(D-v(B)), 0 < v < s - 1, to be s - v and box dimension of Graph(Du(B)), 0 < u < 2 - s, to bes + u is also lim.

Data-Driven Structural Topology Optimization Method Using Conditional Wasserstein Generative Adversarial Networks with Gradient Penalty

Traditional topology optimization methods often suffer from the“dimension curse”problem,wherein the com-putation time increases exponentially with the degrees of freedom in the background grid.Overcoming this challenge,we introduce a real-time topology optimization approach leveraging Conditional Generative Adversarial Networks with Gradient Penalty(CGAN-GP).This innovative method allows for nearly instantaneous prediction of optimized structures.Given a specific boundary condition,the network can produce a unique optimized structure in a one-to-one manner.The process begins by establishing a dataset using simulation data generated through the Solid Isotropic Material with Penalization(SIMP)method.Subsequently,we design a conditional generative adversarial network and train it to generate optimized structures.To further enhance the quality of the optimized structures produced by CGAN-GP,we incorporate Pix2pixGAN.This augmentation results in sharper topologies,yielding structures with enhanced clarity,de-blurring,and edge smoothing.Our proposed method yields a significant reduction in computational time when compared to traditional topology optimization algorithms,all while maintaining an impressive accuracy rate of up to 85%,as demonstrated through numerical examples.

The fractal characteristic change in the Huanghe River Estuary due to the hydrodynamic conditions’variation

The study area lies in the subaqueous delta, which came into being in 1964 - 1976. Oneoil-field road has been built for exploring petroleum to form a wave barrier. The hydrodynarnic conditions on the north side of the road are relatively violent, on the contrary the hydrodynarnic conditions on the south side of the road are nearly placid. This makes the study area a natural laboratory for studying the influence of the hydrodynarnic conditions on the fractal characteristics of the tidal flat. Selecting an area is named Case Ⅰ on the side of stronger hydrodynarnic activities and an area is named Case Ⅱ on the other side. Measuring the topography and sampling and analyzing the granulometrical composition, it is found that the hydrodynarnic conditions have fatal influence on the surface fractal dimensions and the granulometrical fractal dimensions of the area. In Case Ⅰ , which has strong hydrodynarnic conditions, the surface fractal dimensions are obviously larger than those of Case Ⅱ , and the granulometrical fractal dimensions are relatively smaller than those of Case Ⅱ , the surface fractal dimensions of Case Ⅰ decrease quickly with the increase of grid size; the granulometrical fractal dimensions are disperse, while the hydrodynarnic conditions of Case Ⅱ are just reverse. A sampling line and a core sampling on each side of the road are selected. It is found that on the south side of the road the granulometrical fractal dimensions vary regularly in the line and with the depth, the farther apart from the road, the smaller the fractal dimensions, and the deeper the sampling position the larger the fractal dimensions, while granulometrical fractal dimensions on the north side of the road have no such regularity pattern. The mechanism of the influence of the hydrodynarnic conditions on the fractal characteristics is discussed.

Possibilities and challenges of expanding dimensions of waterway downstream of Three Gorges Dam

The waterway in the middle and lower reaches of the Yangtze River has long been known as the Golden Waterway and has served as an important link in the construction of the Yangtze River Economic Belt.Therefore,expanding its dimensions is a significant goal,particularly given the long-range cumulative erosion occurring downstream of the Three Gorges Dam (TGD),which has been concentrated in the dry river channel.With the regulation of the volume from upstream reservoirs and the TGD,the minimum discharge and water level of the river downstream are increasing,and creating favorable conditions for the increase of the depth of the waterway.The discharge compensation effect during the dry season offsets the decline in the water level of the river channel caused by the down-cutting of part of the riverbed,but the minimum navigable water level of the segment near the dam still shows a declining trend.In recent years,several waterway remediation projects have been implemented in the downstream reaches of the TGD and although the waterway depth and width have been increased,the channel dimensions are still insufficient in the Yichang-Anqing reach (with a total length of 1026 km),as compared to the upstream reservoir area and the deep water channel in the downstream tidal reaches.A comprehensive analysis of the water depth and the number and length of shoals in the waterway indicates that its dimensions can be increased to 4.5 m ×200 m and 6.0 m×200 m in the Yichang-Wuhan and Wuhan-Anqing reaches,respectively.This is also feasible given the remediation technologies currently available,but remediation projects need to be coordinated with those for flood prevention and ecological protection.

ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS SATISFYING OPEN SET CONDITION

In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition （OSC）. As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure.

Pointwise dimensions of general Moran measures with open set condition

Recently Lou and Wu obtained the formulas of pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.In this paper,we prove that the result is still true under the open set condition.Due to the lack of the strong separation condition,our approach is essentially different from that used by Lou and Wu.We also obtain the formulas of the Hausdorff and packing dimensions of the Moran measures and discuss some interesting examples.

EXACT NONREFLECTING BOUNDARY CONDITIONS FOR AN ACOUSTIC PROBLEM IN THREE DIMENSIONS

In this paper, nonreflecting artificial boundary conditions are considered for an acoustic problem in three dimensions. With the technique of Fourier decomposition under the orthogonal basis of spherical harmonics, three kinds of equivalent exact artificial boundary conditions are obtained on a spherical artificial boundary. A numerical test is presented to show the performance of the method.

Approximating Conditional Density Functions Using Dimension Reduction

We propose to approximate the conditional density function of a random variable Y given a dependent random d-vector X by that of Y given θ^τX, where the unit vector θ is selected such that the average Kullback-Leibler discrepancy distance between the two conditional density functions obtains the minimum. Our approach is nonparametric as far as the estimation of the conditional density functions is concerned. We have shown that this nonparametric estimator is asymptotically adaptive to the unknown index θ in the sense that the first order asymptotic mean squared error of the estimator is the same as that when θ was known. The proposed method is illustrated using both simulated and real-data examples.

AR模型和分形几何在设备状态监测中的应用研究

状态特征指标对机械的状态监测和故障诊断具有重要意义。本文提出应用机械设备工作状态下噪声信号自回归模型的关联维数来描述设备在不同工作状态下的特征 ,进而实现对状态的监测、识别和分类。文中通过实验证明 ,设备在相同工作状态下 ,噪声信号的AR模型参数具有相近的关联维数 ,在不相同状态下则有明显不同的关联维数。因此关联维数不仅可以作为状态监测与识别和分类的重要依据 ,而且可以作为其他特征提取方法的补充。

计算机辅助公差设计一致性的评价工具——软件量规

在漂移模型、虚拟边界要求、条件公差理论以及ＩＳＯ 和国家标准的公差原则基础上，给出可用于孔轴类零件公差一致性验证的软件量规数学等效式。为基于约束的参数化ＣＡＤ系统中，计算机辅助公差设计的评价提供了理论依据，对促进ＣＡＤ／ＣＡＭ 集成。

微波辐射对净水厂污泥脱水性能及分形结构的影响

对净水厂污泥在2450MHz微波作用下的调质效果进行了研究.结果表明,污泥比阻随着微波功率的增大和辐射时间的增长而下降,700W微波辐射10min能使500ml含水率为98%的污泥比阻下降73%.经微波调质(700W,5min)后,污泥颗粒变得粗大化,30—50μm范围内的污泥颗粒数增多,平均粒径由30.73μm增加至33.29μm;污泥颗粒的分形维数由1.712提高到1.724.

基于分形几何状态监测方法的应用研究

根据二进小波变换原理 ,分析了机械设备噪声信号某一特征尺度下的时域信号分量的分形特性 ,提出可以用分形关联维数描述设备的工作特征 ,进而对状态进行监测。试验表明 ,相同工作状态下 ,某一特征尺度下的时域信号分量有相近的关联维数 ,而在不相同状态下则有明显不同的关联维数。关联维数可以作为机械设备状态分类的重要依据 。

关联维数在设备状态监测中的应用研究

提出用关联维数来定量描述机械设备的工作状态 ,进而对设备进行故障诊断。同时研究了噪声对关联维数计算结果的影响 ,并提出用采样迭代奇异值降噪算法对原始数据进行降噪处理。文中以 ZYB80 A型复合气泵为例 ,计算了气泵在不同工作状态下降噪处理后振动信号的关联维数 ,分析结果表明 ,气泵不同运行情况所对应的关联维数有明显不同 ,因此可以用关联维数区分气泵的运行状态。以关联维数作为故障诊断的依据 。

水动力条件差异导致潮坪分形特征变化实例研究

研究区位于1964～1976年黄河由刁口流路入海时形成的三角洲潮坪。为进行石油开采在潮坪上构筑的交通设施对波浪形成了良好的屏障,水动力条件具有显著差异的屏障两侧潮坪是研究潮坪特征对水动力条件响应的天然实验场所。在屏障两侧各选择一典型区,实测地貌形态,取样品进行粒度成分分析,根据实测资料分析确定潮坪分形特征。发现水动力环境的强弱决定着潮坪的形貌、沉积物粒度分维值的变化规律。水动力环境强的一侧潮坪滩面分维值高,且随着初始计算网格宽度增大迅速降维;表层沉积物粒度分维值小,且离散性大。相反,在另一侧潮坪滩面分维值低,且随着初始计算网格宽度增大分维值无显著变化;表层沉积物粒度分维值高,且具有较好的一致性。当初始计算网格宽度增大到某个值时,两侧潮坪形貌分维值渐趋一致。在屏障两侧各沿一条与屏障大角度相交的测线取样,并各选择一点采取不同深度的样品做分析计算,发现在水动力条件弱的一侧,样品的粒度分维值表现为远离屏障逐步降维、随深度增加分维值增大的规律;相反一侧粒度分维值变化的规律性很不明显。讨论了水动力环境对潮坪分形特征影响机理。

紫色泥岩水热条件下崩解过程的分维特性

以马头山组(K2m)、妥甸组(J3t)和下禄丰组(J1l)自然风干的紫色泥岩为研究对象,分别进行干湿、冷热和干湿冷热3种处理,并运用分维方法分析不同处理下紫色泥岩的崩解特性,发现分维数能比较准确地表征紫色泥岩的崩解过程:分维数越大,岩石破碎程度越高;分维数越小,岩石破碎程度越低。3种紫色泥岩在不同处理方式下崩解的分维数大小都是干湿冷热>干湿>冷热,可见,水热共同作用对母岩崩解的影响明显大于仅有水或热的作用。相同处理方式下3种泥岩的分维数大小为J3t>J1l>K2m,且在干湿和干湿冷热条件下J3t的崩解分维数与K2m和J1l的差异显著,这主要是由这3种泥岩的物理特性、元素组成以及其风化成度所决定的。

基于系统混沌指数的航空发动机状态监测

从混沌理论、分形学的角度研究了航空发动机失稳工作,计算了发动机失稳过程系统混沌特征量的变化.采用小波降噪对压气机压力数据作预处理,重构了系统相空间,改进了关联积分的计算方法,在此基础上采用滑动窗口方法计算了发动机失稳过程中系统李雅普诺夫指数、关联维数的变化.计算结果显示,发动机失稳过程中系统的混沌指数有显著的改变,系统进入失稳状态李雅普诺夫指数增大0.19,而关联维数则减小0.45,表明混沌指数可用于发动机系统的状态监控,亦为发动机失稳运动的特性研究提供了新思路.

轻型木结构房屋用杉木规格材机械应力分等研究

通过测试足尺试件的拉、压、弯力学性能,研究了机械应力分级等级边界条件设置及等级特征值.结果表明:划分MOE区间后建立的强度平均值与弹性模量平均值的回归关系决定系数明显提高,可用于建立强度关系,该关系对机械应力分级的实现具有重要的指导意义;按照GB50005—2003《木结构设计规范》及EN338:2008(E)《结构材强度等级》的规定,在不考虑密度、满足各等级对抗拉及抗压强度特征值要求的情况下,可以将杉木规格材划分为M10,M18,M26这3个等级.

Lyapunov指数计算算法的设计与实现

为了定量分析混沌系统的动力学特性,论文研究了计算Lyapunov指数的Jacobi矩阵算法,并采用Matlab6.5软件平台设计了基于该算法的Lyapunov指数计算软件,算法程序简洁、可读性强、易于移植,GUI编程技术使人机交换能力增强,制作的Lyapunov指数工具箱能够求解非线性动力学系统的Lyapunov指数谱和分数维。最后,分析了迭代次数、计算步长、解法器和初值等因素对计算精度的影响。

絮凝条件对絮体分形结构的影响

在85kg/m3的含沙高浊水中投加阳离子高分子聚合物,借助图像分析技术与沉降技术分析探讨了不同絮凝条件下泥沙絮凝形态学参数:絮体粒径、絮体有效质量密度、絮体自由沉速、浑液面沉速与上清液余浊等的变化规律.利用表征参数“分维”定量控制不同絮凝条件(如搅拌速率、搅拌时间、高分子浓度等)对含沙高浊水絮体结构分形特性的影响.实验证明,不合适的絮凝条件将导致絮体分形构造疏松脆弱,分维值低.絮凝条件合适时(快速絮凝强度为:r1=300r/min,t1=10s;慢速絮凝强度:r2=120r/min,t2=180s;CP浓度:0.1%),絮体分形结构处于最佳状态.该状态下的絮体具有粒径较大、沉速快、有效质量密度高、粒度分布均匀,分维值最高(D3=2.16)的特点.而且,由静沉实验测得浑液面沉速高,上清液余浊也低.泥沙絮体分形结构达最佳时的混凝性能、沉降性能与结构密实性均较理想.