Papers by Keyword: Fractal Model

Abstract: This paper presents an investigation into the complex dynamics and enhanced predictability of organic water pollution using a multifractal methodology. The study utilizes a time series dataset of water pollution measures, where time-series analysis and the Multi-Fractal Detrended Fluctuation Analysis (MFDFA) were individually applied to both Biochemical Oxygen Demand (BOD) and Chemical Oxygen Demand (COD) metrics. By analyzing and comparing the characteristics of each metric, the research establishes a deeper insight into the overall organic pollution dynamics, which informs the subsequent modeling. The MFDFA results were used to accurately estimate the fractal differentiation parameter (d) for the ARFIMA (AutoRegressive Fractionally Integrated Moving Average) model. The resulting forecasts for pollution were evaluated and compared against those obtained from the traditional ARIMA (AutoRegressive Integrated Moving Average) model and a basic ARFIMA fractal model. Comparative analysis, utilizing performance metrics such as Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE), conclusively demonstrates that the methodology integrating multifractal analysis and the ARFIMA fractal model provides an enhancement in predictive accuracy for water pollution time series for metrics where high multifractal evidence was detected through the MFDFA, thereby validating the utility of fractal methods in capturing the underlying complexity and long-memory dependencies of highly heterogeneous environmental processes.

Abstract: In order to study the effects of operating parameters and surface topography on friction factors between the end faces for mechanical seals, a friction factor fractal model between end faces for contact mechanical seals was established based on the contact fractal model and the average film thickness fractal model, adopting fractal parameters to represent surface topography, separating friction into viscous shear friction of liquid film and contact friction of asperities, and representing the effect of actual rough surface on viscous shear stress of liquid film by introducing the contact factor. The influencing factors of friction factor for B104a-70 mechanical seal were analyzed by simulating. Results showed that the friction factor between the surfaces increases with the increases of spring pressure when the end faces are coarser, while the friction factor decreases slightly with the increases of spring pressure when the end faces are smoother. The friction factor between the faces decreases with the increases of the sealed fluid pressure, which increases approximate linearly with the increases of rotating speed, and it increases with the increases of fractal dimension of end faces and the decreases of the characteristic scale factor.

Abstract: In order to research and master the effect of surface topography on average film thickness between the end faces for mechanical seals, average film thickness fractal model between the end faces for mechanical seal was established using fractal parameters charactering surface topography characteristics, based on contact fractal model of the end face for mechanical seal, and solving micro-void volume. Effect of surface topography fractal parameters on average film thickness between the end faces for B104a-70 mechanical seal was analyzed by theoretical calculation. The results showed that fractal dimension D and characteristic length scale G of the end face had a great influence on the average film thickness h₀, and h₀ decreased with the increased of D or decreased of G; h₀ decreased rapidly with the increased of D or with the decreased of G when the end face was coarser, however, it decreased slowly with the increased of D or with the decreased of G when the end face was smoother. In normal working parameters and surface topography fractal parameters range, average film thickness between end faces was in the range of 0.27~1.7μm. Studying on the effect of the change of surface topography on average film thickness has an important significance on the predicting of operating characteristics of end faces during actual operating and the design of end faces for contact mechanical seal.

Abstract: In this article, according to WenShuHua and Zhangxueniang fractal model, we point out the deficiency. Based on the fractal theory and Zhang, Wens contact stiffness fractal model, this paper puts forward Gamma distribution of rough joint surface normal contact stiffness. This paper considers micro convex body for ellipsoid, contact area for elliptic. This is slightly convex body for sphere hypothesis is more close to the actual situation. At the same time by using statistics theory, considering the contact ellipse long, short axis a and b are greater than zero, the assumption of a and b to two-dimensional Gamma distribution, it is more suitable for engineering practice.

Abstract: Aiming at cold-pressed oil cakes of linseed and sunflower seed, the pore fractal characteristics of microstructures have been studied. By combining Hagen-Poiseuille equation with fractal theory, a fractal permeability model for oil cake has been developed. The permeability of linseed and sunflower seed cakes under cold-pressed condition has been measured. It was found that the relative average errors are 12.8% and 16.8% for the soybean cake and sunflower seed cake respectively by comparing the result from the model calculation and experiment.

Abstract: Based on the fractal contact theory, the model about the relation between normal contact stiffness and material properties as well as fractal parameters is established. Then by making use of the relation between fractal parameters and surface roughness, a new method for estimating the normal contact stiffness is put forward. The numerical results indicate that the contact stiffness increases as surface roughness decreases or adhesion rate increases. When the adhesion rate is constant, contact stiffness changes a little while R_a≥6.3μm, but the change is relatively bigger when R_a≤6.3μm. Considering both the cost of surface machining and the influence of contact stiffness on the whole system, the surface roughness is suggested to be R_a=6.3μm. The results provide theoretical supports for vibration isolation analysis with gaskets and the process of low-noise construction.

Abstract: Application of fractal method to establish geological data fractal model is an important way to identify geological anomaly. Using derivative identification method, it can divide the fractal model’s non-scale range respectively. It determines the abnormal areas according to the abnormal lower limit value. In this paper, the geological data of Au element is calculated by "C-A" fractal model in Mohe Heilongjiang province. On the same non-scale range the double logarithmic fitting curve has the similar local slope and the second-order derivative of this curve within the same non-scale range could be slightly fluctuate near zero. Using the threshold , the non-scale ranges can be identified by this method. The abnormal lower limit value identified by this method is lesser than the artificial recognition method. On the Matlab software platform to calculate Au abnormal areas’ dimension value is 2.65, and the element abnormal lower limit value is 2.9. The abnormal areas delineated by this abnormal lower limit value contain all the gold ore sites we have known.

Abstract: Through the analysis and research on three fractal models of normal contact stiffness of joint interfaces, the differences between them can be found. Furthermore, numerical simulation was carried out to obtain the complicated nonlinear relations between normal contact stiffness and the normal load. The results show that the normal contact stiffness increases with the normal load, decreases with G but complicatedly varies with D. According to different fractal dimension, we can chose an appropriate one among the three fractal models of normal contact stiffness of joint interfaces when describing normal contact stiffness of joint interfaces.

Abstract: In order to kinematic simulate the lapping process with the semi-fixed abrasive plate; a fractal modeling of the semi-fixed abrasive lapping abrasive plate’s surface topography is presented in this paper. A numerical procedure for effectively generating the semi-fixed abrasive lapping abrasive plate surface topography is suggested. The procedure is based on the fractal characteristic of the semi-fixed abrasive plate and the fractal dimension was obtained from the measured structure function of the abrasive plate surface used the Digital Microscope Resources Center. Numerical examples are used to illustrate the viability of the approach. It would be powerful to describe the complex interaction of the abrasive plate and workpiece.