Multirange Fractal Analysis on the Negative Correlation between Fractal Dimension of Fractured Surface and Toughness of Materials

Applying the concept of multirange fractals, a new explanation to the Williford’s multifractal curve on the relationship of fractal dimension with fracture properties in materials has been given. It 5hows the importance of factorizing out the effect of fractal structure from other physical causes and separating the appropriate range of scale from multirange

A complexity measure approach based on forbidden patterns and correlation degree

Based on forbidden patterns in symbolic dynamics,symbolic subsequences are classified and relations between forbidden patterns,correlation dimensions and complexity measures are studied.A complexity measure approach is proposed in order to separate deterministic (usually chaotic) series from random ones and measure the complexities of different dynamic systems.The complexity is related to the correlation dimensions,and the algorithm is simple and suitable for time series with noise.In the paper,the complexity measure method is used to study dynamic systems of the Logistic map and the Hénon map with multi-parameters.

Evaluation of Surface Roughness of Aluminum Alloy in Burnishing Process Based on Chaos Theory

Burnishing experiments with different burnishing parameters were performed on a computer numerical control milling machine to characterize the surface roughness of an aluminum alloy during burnishing.The chaos theory was employed to investigate the nonlinear features of the burnishing system.The experimental results show that the power spectrum is broadband and continuous,and the Lyapunov exponentλis positive,proving that burnishing has chaotic characteristics.The chaotic characteristic parameter,the correlation dimension D,is sensitive to the time behavior of the system and is used to establish the corresponding relationship with the surface roughness.The correlation dimension was the largest,when the surface roughness was the smallest.Furthermore,when the correlation dimension curve decreases,the roughness curve increases.The correlation dimension and surface roughness exhibit opposite variation trends.The higher the correlation dimension,the lower the surface roughness.The surface roughness of the aluminum alloy can be characterized online by calculating the correlation dimension during burnishing.

Chaotic Characteristic Analysis of Air Traffic System

Chaotic characteristics of traffic flow time series is analyzed to further investigate nonlinear characteristics of air traffic system.Phase space is reconstructed both by time delay which is built through mutual information,and by embedding dimension which is based on false nearest neighbors method.In order to analyze chaotic characteristics of time series,correlation dimensions and the largest Lyapunov exponents are calculated through Grassberger-Procaccia(G-P)algorithm and small-data method.Five-day radar data from the control center in Guangzhou area are analyzed and the results show that saturated correlation dimensions with self-similar structures exist in time series,and the largest Lyapunov exponents are all equal to zero and not sensitive to initial conditions.Air traffic system is affected by multiple factors,containing inherent randomness,which lead to chaos.Only grasping chaotic characteristics can air traffic be predicted and controlled accurately.

Bi-prism-based single-lens three dimensional digital image correlation system with a long working distance: Methodology and application in extreme high temperature deformation test

As a novel three dimensional digital image correlation(3 D DIC) method, the bi-prism-based single lens(BSL) 3 D DIC method has been proposed and developed in recent years. Making use of a bi-prism, this method is able to perform a 3 D DIC measurement using only a single camera. Thus, the integration level of a BSL 3 D DIC system could be much higher than that of the double-camera3 D DIC system. In this paper, using a small-angle bi-prism and a camera with a longer focal length, a special BSL 3 D DIC system with a long working distance is designed for measurements in extreme environments. The principle of the system is first studied,and practical methods are then proposed for the system set-up and the determination of system parameters. Then, feasibility of the measurement system is verified by out-of-plane rigid-body translation tests. Finally, the BSL 3 D DIC system is proven to be capable of combining with a high-temperature testing instrument to perform deformation tests in a high-temperature environment of up to 1500°C.

Wavelet denoising and nonlinear analysis of solids concentration signal in circulating fluidized bed riser

Particles,particle aggregates,and reactor walls complicate the dynamic microstructures of circulating fluidized beds(CFBs).Using local solids concentration data from a 10-m-high and 76.2-mm-inner-diameter riser with FCC(Fluid Catalytic Cracking)particles(dp=67μm,ρp=1500 kg/m^3),this paper presents an improved denoising process for use before nonlinear chaos analysis.Using the soft-threshold denoising method in the wavelet domain with experimental empty bed signals as base data to estimate the denoising threshold,an efficient denoising algorithm was proposed and used for the dynamic signals in CFBs.Analysis shows that for the local solids concentration time series,high-frequency fluctuations may be one of the system properties,while noise interference can also make a low-frequency contribution.An exact denoising method is needed in such cases.The correlation dimension and Kolmogorov entropy were calculated using denoised data and the results showed that the particle behavior in the CFB is highly complex.Generally,two correlation dimensions coexist in a low-flux CFB.The first correlation dimension is low and corresponds to small-scale fluctuations that reveal a high-frequency pseudo-periodic movement,but the second correlation dimension is high and corresponds to large-scale fluctuations that indicate multi-frequency movements,including particle aggregation and breakage.At the same axial level,the first correlation dimensions change slightly with radial position,and the main tendency is high at the center but slightly lower near the wall.However,the second correlation dimensions show large changes along the radial direction,are again high in the core region,and after r/R≥0.6(r as radial position,R as radius of the riser),the dimensions clearly drop down.This indicates that the particle behavior is more complex and has higher degrees of freedom at the center,but clusters near the wall are restrained to some degree because of wall effects.