VIBRATION ANALYSIS OF DIESEL'S COMBU SION BASED ON FRACTAL THEORY

Self-similarity of diesel's combustion process is analyzed.Vibration signals of combustion are picked up from the cylinder wall,and correlation fractal dimension D is calculated by using G - P algorithm in fractal theory. Parameters which influence D are investigated.At the same time, D can present cylinder's combustion condition to some extent.Thus,D can be used as a diagnostic parameter and used in diesel's fault diagnosis.

Application Study of Fractal Theory in Mechanical Transmission

Mechanical transmissions are applied widely in various electrical and mechanical products, but some qualities of some high-end products can＇t meet people＇s demand, and need to be improved with some new methods or theories. The fractal theory is a new mathematic tool, which provides a new approach for the further study in the area of the mechanical transmission, and helps to solve some problems. The basic contents of the fractal theory are introduced firstly, especially the two important concepts, the self-similar fractal and the fractal dimension. Then, the deferent application of the fractal theory in this area are given to display how to further the study and improve some important characteristics of the mechanical transmission, such as contact surfaces, manufacturing precise, friction and wear, stiffness, strength, dynamics, fault diagnosis, etc. Finally, the problems of the fractal theory and its application are discussed, and some weaknesses, such as the calculation capacity of the fractal theory is not strong, are pointed out. Some new solutions are suggested, such as combining the fractal theory with the fuzzy theory, the chaos theory and so on. The new application fields of the fractal theory in the area of the mechanical transmission are proposed.

Elastoplastic Contact Mechanics Model of Rough Surface Based on Fractal Theory

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ~b, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.

Advances in applied studies of fractal theory in geography in China

The fractal theory put forward by American mathematician B B Mandelbrot (1967) supplies an effective approach to solve complex problems. The complex problems in geography have become the main positive study field of fractal theory. Based on the works of China's geographers and the summarization of contents of fractal theory, the authors comment on the present situation of its applications to almost every branch of geography and discuss the related problems and the prospects of fractal study in geography.

Use of digital image analysis combined with fractal theory to determine particle morphology and surface texture of quartz sands

The particle morphology and surface texture play a major role in influencing mechanical and hydraulic behaviors of sandy soils. This paper presents the use of digital image analysis combined with fractal theory as a tool to quantify the particle morphology and surface texture of two types of quartz sands widely used in the region of Vitória, Espírito Santo, southeast of Brazil. The two investigated sands are sampled from different locations. The purpose of this paper is to present a simple, straightforward,reliable and reproducible methodology that can identify representative sandy soil texture parameters.The test results of the soil samples of the two sands separated by sieving into six size fractions are presented and discussed. The main advantages of the adopted methodology are its simplicity, reliability of the results, and relatively low cost. The results show that sands from the coastal spit(BS) have a greater degree of roundness and a smoother surface texture than river sands(RS). The values obtained in the test are statistically analyzed, and again it is confirmed that the BS sand has a slightly greater degree of sphericity than that of the RS sand. Moreover, the RS sand with rough surface texture has larger specific surface area values than the similar BS sand, which agree with the obtained roughness fractal dimensions. The consistent experimental results demonstrate that image analysis combined with fractal theory is an accurate and efficient method to quantify the differences in particle morphology and surface texture of quartz sands.

Application of the fractal theory for evaluating effects of coal comminution by waterjet

Comminution of coal to ultrafine sizes by high-pressure waterjet provides a novel method for preparation of coal-water fuels for next generation,near-zero emission electric power generation.The particle size distribution(PSD)of ground coal is a key parameter in the preparation of slurries as it determines the settling behavior of the particles and viscosity of the coal-water mixture.There are several methods available for representation and evaluation of particle size analysis data.However,fractal theory provides a means by which the entire PSD of comminuted materials can be quantified by using of a specific and exact value.In this paper,a volume-based fractal model was deduced to characterize the PSD of the coal which is ground in a specially designed comminution cell.During the size reduction process,the inlet pressures up to 276 MPa were used.

Dynamic development model for long gap discharge streamer-leader system based on fractal theory

Establishing a long air gap discharge model considering the streamer-leader transition and randomness of the discharge path is of great signiflcance to improve the accuracy of discharge characteristic prediction and optimize external insulation design.Based on fractal theory and thermal ionization theory of streamer-leader transition,this work establishes a dynamic development model for the long air gap discharge streamer-leader system,which includes streamer inception,streamer development,leader inception,development of streamer-leader system and flnal jump.The positive discharge process of a 3 m rod plate is simulated to obtain the fractal distribution of the discharge path and the law of leader development for comparison with the discharge test results.The results show that the simulation model is similar to test results in the development characteristics of leader path distribution,each stage time and leader velocity.Finally,a simulation calculation of a 50%breakdown voltage of the rod-plate gap and ball-plate gap is carried out,with results fairly consistent with test data,proving the effectiveness and practicality of the model.

Contact Model of Revolute Joint with Clearance Based on Fractal Theory

The contact sti ness of a mechanical bonding surface is an important parameter in determining the normal and radial contact force. To improve the calculation accuracy of the contact force model, the surface roughness of the bonding surface and the energy loss that necessarily occurs during the impact process should be considered com?prehensively. To study the normal contact force of a revolute joint with clearance more accurately in the case of dry friction, a nonlinear sti ness coe cient model considering the surface roughness was established based on fractal theory, which considers the elastic, elastic?plastic, and plastic deformations of the asperities of the contact surface during the contact process. On this basis, a modified nonlinear spring damping model was established based on the Lankarani–Nikravesh contact force model. The laws influencing the surface roughness, recovery coe cient, initial velocity, and clearance size on the impact force were revealed, and were compared with the Lankarani–Nikravesh model and a hybrid model using MATLAB. The maximum impact force was obtained using a modified contact force model under di erent initial velocities, di erent clearances, and di erent degrees of surface roughness, and the calculated results were then compared with the experiment results. This study indicates that the modified model can be used more widely than other models, and is suitable for both large and small clearances. In particular, the modified model is more accurate when calculating the contact force of a revolute joint with a small clearance.

Novel welding image processing method based on fractal theory

Computer vision has come into used in the fields of welding process control and automation. In order to improve precision and rapidity of welding image processing, a novel method based on fractal theory has been put forward in this paper. Compared with traditional methods, the image is preliminarily processed in the macroscopic regions then thoroughly analyzed in the microscopic regions in the new method. With which, an image is divided up to some regions according to the different fractal characters of image edge, and the fuzzy regions including image edges are detected out, then image edges are identified with Sobel operator and curved by LSM (Lease Square Method). Since the data to be processed have been decreased and the noise of image has been reduced, it has been testified through experiments that edges of weld seam or weld pool could be recognized correctly and quickly.

Application of Fractal Theory in Simulation of Ferromagnetic Elements' Hysteresis Loop in Transformer

The simulation of the transformer transient is one of the indispensable qualifications for improving the performance of transformer protection, the key technique of the transformer's transient simulation is the treatment of ferromagnetic elements' loop. Thus the shapes of the primary hysteresis loop and each internal secondary hysteresis loop in the identical magnetism conducting are analyzed, and then it is proposed that there are some fractal characteristics in the relation between them. The fractal phenomenon of the ferromagnetic elements' hysteresis loop in the transformer's transient simulation is first brought forward, the mutuality between the ferromagnetic elements' primary hysteresis loop and its secondary hysteresis loops is revealed in mechanism by using the fractal theory. According to the iterated function system of fractal theory, the secondary hysteresis loops can be generated by the iterative calculation of the primary loop. The simulation results show the validity of this idea.

Development and application of geochemical data processing system based on fractal theory

GC-GIS system is a geochemical data processing system based on fractal theory. The system realized quantity statistics function by calling Surfer and MapInfo software, and it is compiled with Visual Basic language. This system is designed to integrate the functions both quantity statistics of Surfer and spatial data management of MapInfo. A new algorithm of fractal is added up to GC-GIS. Taking example for Weichang region of Hebei to test the system, the processing results show that the model can match the real distribution of mine well.

A semi-analytical model for coupled flow in stress-sensitive multi-scale shale reservoirs with fractal characteristics

A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes due to stress sensitivity, which plays a crucial role in controlling pressure propagation and oil flow. This paper proposes a multi-scale coupled flow mathematical model of matrix nanopores, induced fractures, and hydraulic fractures. In this model, the micro-scale effects of shale oil flow in fractal nanopores, fractal induced fracture network, and stress sensitivity of multi-scale media are considered. We solved the model iteratively using Pedrosa transform, semi-analytic Segmented Bessel function, Laplace transform. The results of this model exhibit good agreement with the numerical solution and field production data, confirming the high accuracy of the model. As well, the influence of stress sensitivity on permeability, pressure and production is analyzed. It is shown that the permeability and production decrease significantly when induced fractures are weakly supported. Closed induced fractures can inhibit interporosity flow in the stimulated reservoir volume (SRV). It has been shown in sensitivity analysis that hydraulic fractures are beneficial to early production, and induced fractures in SRV are beneficial to middle production. The model can characterize multi-scale flow characteristics of shale oil, providing theoretical guidance for rapid productivity evaluation.

Reexamination of Correlations for Nucleate SiteDistribution on Boiling Surface by Fractal Theory

Nucleate site distribution plays an essential role in nucleate boiling process. In this paper1 it is pointed out that the size and spatial distribution density of nucleate sites presented on real boiling surface can be described by the normalized fractal distribution function, and the physical meaning of parameters involved in some experimental correlations proposed by early investigations are identified according to fractal distribution function. It is further suggested that the surface micro geometry characteristics such as the shape of cavities should be described and analyzed qualitatively by using fractal theory.

Spatial Behavior Characteristics of Land Use based on Fractal Theory:Taking Poyang Lake Area as an Example

Landscape morphology can reflect the spatial behavior of land use.Using the Poyang Lake area as an example,the landscape pattern characteristics in 1995,2000,2015,and 2018 are determined by calculating the fractal dimension,fractal stability,patch density,patch shape fragmentation,and landscape isolation,and fractal theory is used to analyze the spatial behavior of land use.The results show that building land was the land use type which consistently had the highest fractal dimension,but the fractal dimension of building land shows a downward trend,indicating that the spatial form of building land gradually developed in an orderly direction under the action of land use spatial behavior.Paddy,dryland,and forested land were the land use types which always had the lowest fractal dimension,and they are in unstable states.The calculation results of patch density,patch shape fragmentation index,and landscape isolation index supported the conclusions of the fractal analysis.One recommendation for realizing the rational layout of the land is to reduce the fractal dimension of building land through scientific and reasonable planning and to guide the orderly development of building land.For natural landscapes such as forested land,shrub forest land,high-coverage grassland,and water area,their fractal dimensions should be increased to reduce human interference and maintain their stability.Finally,the results of this study suggest that the fractal dimension should be introduced into the National Spatial Planning,and used as an index for evaluating the rationality of the regional land use pattern.

MULTI-SCALE NUMERICAL MODEL FOR SIMULATING CONCRETE MATERIAL BASED ON FRACTAL THEORY

A new multi-scale numerical model is presented using the fractal theory and adopting FEM to simulate the failure of concrete.The relation between the fractal box dimension in large scale and the damage to concrete in small scale is deduced.And the evolutionary process of elastic modulus and strength in small scale is given.Consequently,the multi-scale numerical model is proposed to describe the constitutive relation of concrete between small scale and large scale.A two-dimensional static analysis of a concrete block is performed by using this model and the calculation result is discussed.The propagation of cracks of the concrete block is also studied.

Comments on "Reexamination of Correlations for Nucleate Site Distribution on Boiling Surface by Fractal Theory

In recently published paper by Yang Chunxin[1], I reexamined the paper. On page 128, the paper 'pointed out that the size and spatial distribution density of nucleation sites presented on real boiling surface can be described by the normalized fractal distribution function, and the physical meaning of parameters involved in some experimental correlations proposed by early investigations are identified according to fractal distribution'. However, the definition on fractal dimension given by Yang[1] is highly questionable, and the results obtained by Yang are contradictory to the basic fractal theory. Here are my comments:

Multi-scale pore fractal characteristics of differently ranked coal and its impact on gas adsorption

Well-developed pores and cracks in coal reservoirs are the main venues for gas storage and migration.To investigate the multi-scale pore fractal characteristics,six coal samples of different rankings were studied using high-pressure mercury injection(HPMI),low-pressure nitrogen adsorption(LPGA-N2),and scanning electron microscopy(SEM)test methods.Based on the Frankel,Halsey and Hill(FHH)fractal theory,the Menger sponge model,Pores and Cracks Analysis System(PCAS),pore volume complexity(D_(v)),coal surface irregularity(Ds)and pore distribution heterogeneity(D_(p))were studied and evaluated,respectively.The effect of three fractal dimensions on the gas adsorption ability was also analyzed with high-pressure isothermal gas adsorption experiments.Results show that pore structures within these coal samples have obvious fractal characteristics.A noticeable segmentation effect appears in the Dv1and Dv2fitting process,with the boundary size ranging from 36.00 to 182.95 nm,which helps differentiate diffusion pores and seepage fractures.The D values show an asymmetric U-shaped trend as the coal metamorphism increases,demonstrating that coalification greatly affects the pore fractal dimensions.The three fractal dimensions can characterize the difference in coal microstructure and reflect their influence on gas adsorption ability.Langmuir volume(V_(L))has an evident and positive correlation with Dsvalues,whereas Langmuir pressure(P_(L))is mainly affected by the combined action of Dvand Dp.This study will provide valuable knowledge for the appraisal of coal seam gas reservoirs of differently ranked coals.

Pressure transient analysis of multiple fractured horizontal wells in naturally fractured unconventional reservoirs based on fractal theory and fractional calculus

Currently,most models for multiple fractured horizontal wells(MFHWs)in naturally fractured unconventional reservoirs(NFURs)are based on classical Euclidean models which implicitly assume a uniform distribution of natural fractures and that all fractures are homogeneous.While fractal theory provides a powerful method to describe the disorder,heterogeneity,uncertainty and complexity of the NFURs.In this paper,a fractally fractional diffusion model(FFDM)for MFHWs in NFURs is established based on fractal theory and fractional calculus.Particularly,fractal theory is used to describe the heterogeneous,complex fracture network,with consideration of anomalous behavior of diffusion process in NFURs by employing fractional calculus.The Laplace transformation,line source function,dispersion method,and superposition principle are used to solve this new model.The pressure responses in the real time domain are obtained with Stehfest numerical inversion algorithms.The type curves of MFHW with three different outer boundaries are plotted.Sensitivity analysis of some related parameters are discussed as well.This new model provides the relatively more accurate and appropriate evaluation results for pressure transient analysis for MFHWs in NFURs,which could be applied to accurately interpret the real pressure data of an MFHW in field.

Fractal Evolving Theory and Growing Model of Olefin Polymerization Process

The surface morphology of Ti-Mg supported catalyst and the polyethyleneparticles are studied using scanning electron microscope(SEM) technology. The results show thateithen the catalyst's surface or polymer particle's surface is irregular and has fractalcharacteristics, which can be described by fractal parameter. The more interesting discovery is thatthe surface fractal dimension values of the polymer particles vary periodically with thepolymerization time. We call this phenomenon fractal evolution, which can be divided into the'revolution' stage and the 'evolution' stage. And then we present polymerization fractal growingmodel (PFGM), and successfully describe and/or predict the whole evolving process of thepolyethylene particle morphology under the different slurry polymerization (includingpre-polymerization) conditions without H_2.

Fractal evolution mechanism of rock fracture in undersea metal mining

Through rock mechanics test, similar simulation experiment, borehole photographic observation of rock fissure, numerical simulation calculation of plastic zone distribution and deformation monitoring of rock mass during undersea mining, the fractal evolution mechanisms of rock fracture in undersea metallic deposits of Sanshandao Gold Mine were studied by fractal theory. The experimental researches on granite mechanics test in undersea deposit indicate that with the increase of load, the granite deformation energy and the fractal dimension of acoustic emission(FDAE) increase gradually. However, after reaching the peak stress of specimen, the fractal dimensions of acoustic emission(FDAEs) decrease and the granite specimen fails. Therefore, the fractal dimension evolution of rock failure can be divided into four stages, which are fissure inoculation stage, fissure growth stage, fissure expansion stage and fracture instability stage, respectively. By calculating and analyzing the damage photographs of rock specimens in Sanshandao Gold Mine, the fractal dimension of rock fissure is 1.4514, which is close to the average value of FDAE during granite destruction, i.e., 1.4693. Similar simulation experiments of undersea mining show that with the excavation proceeding, the FDAE in rock stratum increases gradually, and when the thickness of the isolation roof is less than 40 m, the FDAE begins to decrease, and meanwhile the sign of water inrush emerges. The numerical simulation researches on the plastic zone distribution of undersea mining in Sanshandao Gold Mine indicate that the fractal dimension of plastic zone(FDPZ) where the failure characteristics occur is 1.4598, close to the result of similar simulation experiment of 1.4364, which shows the sign of water inrush. Meanwhile, the thickness of the isolation roof for undersea mining should be more than 40 m, which is consistent with the results of similar simulation experiment. In Sanshandao Gold Mine, the rock fissures in undersea mining were observed by borehole photography and the rock mass deformation was monitored by multi-point displacement meters, and at the same time the fractal dimensions of strata borehole fissure distribution and energy release ratio(ERR) of rock mass were calculated by fractal principle, which are 1.2328 and 1.2685, respectively. The results demonstrate that rock deformation and fissure propagation are both in the second stage of fissure growth, and have not reached the fourth stage of fracture instability. Therefore, the conclusion can be obtained that the undersea mining in Sanshandao Gold Mine is safe at present.