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Pipelines are seriously corroded due to the close distance between pipelines and high voltage transmission lines. The purpose of this paper is to study the influence of alternating current (AC) on corrosion behavior of X80 pipeline steel in coastal soil solution.

The corrosion behavior of X80 steel under different AC densities in coastal soil solution was investigated by electrochemical measurements and image processing technology. Furthermore, a quantitative description model of AC corrosion through fractal dimension of corrosion image was established.

The results show that under low AC density the X80 steel is mainly uniform corrosion, and once AC density reaches 150 A/m², the corrosion morphology gradually turns to pitting corrosion with irregular circle. For another aspect, the fractal dimension of corrosion images shows that the two/three-dimensional fractal dimension increase with the increase of AC density, presenting a linear and an exponential relationship respectively. In addition, the variation of the three-dimensional fractal dimension is the same as that of average corrosion rate. The threshold of the increasing trend of fractal dimension as well as corrosion type is 150 A/m².

The investigation provides a quantitative method to describe AC corrosion morphology through fractal dimension. Furthermore, the method is of benefit to process corrosion images automatically.

The Hurst exponent has been very important in telling the difference between fractal signals and explaining their significance. For estimators of the Hurst exponent, accuracy and efficiency are two inevitable considerations. The main purpose of this study is to raise the execution efficiency of the existing estimators, especially the fast maximum likelihood estimator (MLE), which has optimal accuracy.

A two-stage procedure combining a quicker method and a more accurate one to estimate the Hurst exponent from a large to small range will be developed. For the best possible accuracy, the data-induction method is currently ideal for the first-stage estimator and the fast MLE is the best candidate for the second-stage estimator.

For signals modeled as discrete-time fractional Gaussian noise, the proposed two-stage estimator can save up to 41.18 per cent the computational time of the fast MLE while remaining almost as accurate as the fast MLE, and even for signals modeled as discrete-time fractional Brownian motion, it can also save about 35.29 per cent except for smaller data sizes.

The proposed two-stage estimation procedure is a novel idea. It can be expected that other fields of parameter estimation can apply the concept of the two-stage estimation procedure to raise computational performance while remaining almost as accurate as the more accurate of two estimators.

This paper aims to study the change rule of sintered iron friction properties under high temperature and establish the model to predict the friction coefficient.

The morphological measurements of sintered iron material with four different oxidation degrees are carried out. A prediction model of friction coefficient in high temperature oxide growth stage for sintered iron material is established based on the theory of flash temperature and adhesion friction. The relationship between friction coefficient and the key parameters is found through the test fitting.

The surface topography changes with oxidative wear. The wear debris will be compacted and sintered again to form a composite oxide layer with the temperature increasing. The validity and accuracy of proposed model are tested using the friction coefficient and temperature experiments. Results are in reasonable agreement with those obtained using values of load commonly used.

The significance lies in the change mechanism of high temperature friction characteristic is clarified. Three friction stages related to temperature of dry friction are put forward for sintered iron, and a meaningful reference is provided by the established model for high-temperature performance design of sintered iron friction material.

Since the term was first coined in 1977, fractals seem to have pervaded every branch of science. Attempts to explain what fractals are and what they are being used for. Are they a fad or are they really useful? Considers factors including quantitative measurement, image compression and computer graphics. Concludes that the future will see an increase in the use of fractal graphics.

The purpose of this paper is to explore the variation law between the clay microstructure and macro external force by using soil scanning electron microscope (SEM) images.

First, SEM images of clay were pre-processed by MATLAB, and quantitative statistical parameters such as directional probability entropy, fractal dimension and shape factor are extracted. Second, the distribution force model was proposed, considering that the microscopic parameters of soil particles were independent of each other, and the distribution coefficient was determined according to the analytic hierarchy process (AHP). Then, the fitted formula of quantitative statistical parameters based on the distribution force model was obtained by taking the macroscopic distribution force as independent variable and the microscopic parameters of soil particles as dependent variable. Finally, the correctness of corresponding fitting formula was verified.

The results showed that the change of external consolidation pressure has great influence on the directional probability entropy and fractal dimension, while the shape factor reflecting the regular degree of soil particle shape is less sensitive to the consolidation pressure. The fitting formula has high accuracy, and mostly the R value can reach more than 0.9. All the data have passed the test, which proves that the distribution force model proposed in this paper is rational.

The model can be used to connect the macroscopic stress of soil with the micro-structure deformation of soil particles through mathematical formula, which can provide reference for engineering practice.

Digital design technologies play a significant role in assisting the designer through conceptual architectural design. Computer supported design systems can generate various images at the early design phase and can contribute to seeking alternative architectural forms. Currently, different design approaches are being employed in the formation of architectural products. Examples of architecture that produce unusual forms are often encountered within unique conceptual approaches. The development of new design examples is supported by the digital production of forms, and three-dimensional models through varying geometric approaches. In this study, a design approach that uses computer aided architectural design to produce architectural forms will be suggested. This approach utilizes principles existing in the unique fractal dimension of elements based on a vocabulary relevant to a specific architectural language. By relying on the fractal dimension and features of an existing architectural pattern, this generative design approach supports creativity in the production of new forms. The proposed approach is evaluated as a creative tool in architectural design. The subject of architecture; buildings, spaces, surroundings, symbols of that particular society are also the elements of a meta-language which creates a fractal geometry based relation. It is possible to analyse this relation through a fractal geometry-based principle. In short, a fractal geometrical generative method is suggested. Also, recently-surfaced discussions about "Chaos Theory" and its effects on the design process via "Chaos and Self - Similarity" are studied. The significance of these different phenomena and disciplines upon architectural design are also studied for developing a possible creative tool.

Frank Lloyd Wright's famous house Fallingwater has been the subject of enduring scholarly debate centred on the allegedly clear parallels between its form and that of its surrounding natural setting. Despite these claims being repeated many times, no quantitative approach has ever been used to test this argument. In response, this paper uses a quantitative method, fractal analysis, to measure the relationship between the architecture of Fallingwater and of its natural surroundings.

Using fractal dimension analysis, a computational method that mathematically measures the characteristic visual complexity of an object, this paper mathematically measures and tests the similarity between the visual properties of Fallingwater and its natural setting. Twenty analogues of the natural surroundings of Fallingwater are measured and the results compared to those developed for the properties of eight views of the house.

Although individual results suggest various levels of visual similarity or difference, the complete set of results do not support the claim that the form of Frank Lloyd Wright's Fallingwater exhibits clear visual similarities to the surrounding landscape.

In addition to testing a prominent theory about Wright's building for the first time, the paper demonstrates a rare application of fractal analysis to interpreting relations between architecture and nature.

Wolverine hairs with superior heat transfer properties have been used as fur ruffs for extreme cold-weather clothing. In order to understand the exclusive mechanism of wolverine surviving in the cold areas of circumpolar, the purpose of this paper is to establish a one-dimensional fractional heat transfer equation to reveal the hidden mechanism for the hairs, and also calculate the fractal dimension of the wolverine hair using the box counting method to verify the proposed theory. The observed results (from the proposed model) found to be in good agreement with the box counting method. This model can explain the phenomenon which offers the theoretical foundation for the design of extreme cold weather clothing.

The authors calculated the fractal dimension of the wolverine hair using the box counting method to verify the proposed theory. The observed results (from the proposed model) found to be in good agreement with the box counting method.

The box counting method proves that the theoretical model is applicable.

The authors propose the first heat transfer model for the wolverine hair.

The objective of the present work is to find an alternative approach for gearbox condition monitoring using wear particle characterization incorporated with image vision systems.

It is a quite well‐known phenomenon that wear generates whenever two metallic bodies have contact with each; other hence the present work tries to investigate the effect of improper lubrication in the gearbox due to wear particle generation between gear wheels. Since the identification of wear for machine condition monitoring needs much expertise knowledge and is time‐consuming using the conventional process, fractal mathematics with image morphological analysis has been utilized to overcome this situation in the present work.

The type of wear has been found for the present method by utilizing the lubricant used in the system ferrographically and a great deal of image processing has been done to characterize the type of particle so that the proper maintenance strategy can be undertaken.

Wear particle characterization is a quite common method in maintenance engineering, especially when fault diagnosis of any equipment is concerned. In the present work, the CCD acquisition of the images has been done for different particles, but one analysis amongst them has been shown in this paper. Among all other methodologies, the new technique of fractal mathematics has been used in the present work to minimize the imaging hazards and to make the system more user‐friendly.

The purpose of this paper is to clarify the growth behavior of fatigue cracks on bionic coupling surface of vermicular cast iron.

The thermal fatigue cyclic experiments were carried out on the bionic specimens processed by laser bionic treatment, in which the thermal fatigue was generated by heating at 600°C ± 5°C and cooling at 25°C ± 5°C. The thermal fatigue cracks of bionic units were analyzed using fractal theory. The relation between fractal dimensions of thermal fatigue cracks and thermal fatigue cycles was discussed.

The results show that the fractal dimensions can better characterize the fatigue crack growth behavior on bionic coupling surface of vermicular cast iron.

The fractal theory is first used to discuss the growth behavior of fatigue cracks on bionic coupling surface of vermicular cast iron, which is processed by laser bionic treatment.