Fractal Theory Model Research Articles

Multi-Point Seawall Settlement Prediction with Limited Data Volume Using an Improved Fractional-Order Grey Model

Settlement prediction based on monitoring data holds significant importance for engineering maintenance of seawalls. In practical engineering, the volume of the collected monitoring data is often limited due to the restrictions of devices and engineering budgets. Previous studies have applied the fractional-order grey model to time series prediction under the situation of limited data volume. However, the performance of the fractional-order grey model is easily affected by the inappropriate settings of fractional order. Also, the model cannot make dynamic predictions due to the characteristic of fixed step size. To solve the above problems, in this paper, the genetic algorithm with enhanced search capabilities was employed to solve the premature convergence problem. Additionally, to solve the problem of the fractional-order grey model associated with fixed step size, the real-time tracing algorithm was introduced to conduct equal-dimensionally recursive calculation. The proposed model was validated using monitoring data of four monitoring points at Haiyan seawall in Zhejiang province, China. The prediction performance of the proposed model was then compared with those of the fractional-order GM(1,1), integer-order GM(1,1), and fractal theory model. Results indicate that the proposed model significantly improves the prediction performance compared to other models.

Pore structure characterization and permeability prediction of uranium-bearing sandstone based on digital core

The permeability of the ore-bearing layer is an important indicator affecting the in-situ leaching (ISL) of uranium-bearing sandstone, which is related to various factors such as pore shape, distribution, and size. In order to study the effect of pore structure on seepage in low-permeability uranium-bearing sandstone, CT scanning tests were conducted to create a 3D digital core based on scanning images and to calculate the fractal dimension using the box counting dimension method, which integrated fractal theory to define the core samples' pore structure. The permeability prediction was realized based on the porosity-permeability model and the fractal theory model. Results indicated that this type of sandstone is obviously characterized by pore connectivity, large differences in distribution, and strong microscopic inhomogeneity. The pores are dominated by micro- and nano-pores, as well as small pores, accounting for 90 %; macropores are few in number, but the diameters of their single pores are large. The distribution of pore structure in this type of sandstone exhibits a good fractal characteristic; the three-dimensional fractal dimensionality is 2.044–2.310. The porosity-permeability model was established, and permeability prediction was realized by combining the fractal theory to provide theoretical support for determining the values of well field parameters in ISL.

Landslide Hazard Assessment Methods along Fault Zones Based on Multiple Working Conditions: A Case Study of the Lixian–Luojiabu Fault Zone in Gansu Province (China)

Traditional landslide hazard assessment methods generally use the same evaluation model to carry out assessments under different working conditions. Due to the differences in landslide influence factors and model calculation methods considered under different working conditions, the evaluation results obtained using traditional methods are different from those of real-world scenarios. Therefore, research on optimal landslide hazard assessment methods for different working conditions is important for disaster prevention and mitigation in areas along fault zones. Taking the section along the Lixian–Luojiabu fault zone in Gansu province in China as the research area, a landslide hazard assessment was carried out under rainfall and earthquake conditions. A method based on the fractal theory–information coupling model is proposed for the rainfall condition, and a method based on an improved Newmark model considering matric suction is proposed for the earthquake condition. Under the rainfall condition, a landslide hazard assessment was carried out using the information model, the logistic regression model, the fractal theory model, the logistic regression–information coupling model and the fractal theory–information coupling model. Meanwhile, under the earthquake condition, an assessment was carried out using the traditional Newmark model and the improved Newmark model considering matric suction. Finally, the ROC curve and Kappa coefficient were used to test the accuracy of these evaluation models and to determine the optimal model under different working conditions. The results showed that the fractal theory–information coupling model had the largest AUC value and Kappa coefficient value under the rainfall condition (0.856 and 0.807, respectively). The test value of the logistic regression–information coupling model was second, and the values of the other three models were all lower than 0.8. This shows that the evaluation of the fractal theory–information coupling model is better than those of the other models under the rainfall condition. The AUC value and Kappa coefficient of the improved Newmark model under the earthquake condition were 0.805 and 0.794, respectively, which were larger than the test values of the traditional Newmark model. This shows that the evaluation of the proposed model is better than that of the traditional Newmark model under the earthquake condition. These research results provide a reference for landslide hazard assessments in areas with similar characteristics.

Machine learning and fractal theory models for landslide susceptibility mapping: Case study from the Jinsha River Basin

The quality of “non-landslide” negative samples may result in unreasonable prediction results for machine learning (ML) models. The aim of this study is to improve the performance of ML models by perfecting the quality of “non-landslide” samples in landslide susceptibility modelling so as to produce more reliable susceptibility maps. The middle and lower reaches of Jinsha River basin (MLRJB) were chosen as the study area, and the elevation, slope aspect, curvature, lithology, distance to faults, slope of slope, slope of aspect, precipitation, land use, and NDVI were considered as predisposing factors for landslide susceptibility mapping. Firstly, three “non-landslide” samples are randomly selected from the low-slope area, landslide-free area and very low susceptibility area based on fractal theory (FT) model generation, and then three sample scenarios are constructed with 4445 landslide positive samples. Next, the performance of cross-application of three sample scenarios in the support vector machines (SVM) and naïve Bayes (NB) models are compared and evaluated based on the statistical indicators such as accuracy, recall, precision, receiver operating characteristic (ROC) curve, and area under the ROC curve (AUC). The evaluation results show that the “non-landslide” negative samples generated on the basis of FT model are more reasonable and that the hybrid method supported by FT and ML models exhibits the highest prediction efficiency, around 94% overall accuracy produced by scenario-FT, followed by scenario-SS (87%) and scenario-RS (65%). Finally, with the validation of landslide and unstable slopes data, the landslide susceptibility map produced by the hybrid method composed of FT model and the SVM model is the ultimate output product for landslide prevention.

RESEARCH OF NORMAL CONTACT STIFFNESS OF STRADDLE-TYPE MONORAIL TYRES BASED ON FRACTAL THEORY

The contact stiffness of on the rough surface of tread interaction (tire-track) ,a significant parameter for the tire-track contact surface, gives rise to direct influences on stiffness and noises of tyres. There is no sufficient theoretical support for the wheel face design due to lack of research on this parameter. To solve this problem, an innovative method based on the fractal theory and the Hertz contact theory is proposed to estimate tread interaction contact stiffness. The fractal theory model is established to research the influencing factors on normal contact stiffness on the tread surface. Finite element analysis and physical tests have been conducted to make comparisons about the model. According to research results, there is a non-linear relationship between the contact stiffness and the fractal dimension. The research provides theoretical basis for tyre dynamics of straddle-type monorail vehicles and design of the track contact dynamics.

The deformation analysis, prediction, and experiment verification for thin-wall part assembly based on the fractal theory model with WNNM

Under the load conditions of clamping force and riveting force, the part deformation problems are induced in the assembly process. For the component deformation problems of the thin-wall part assembly, in this paper, from the viewpoint of micro-aspect, the fractal theory model is proposed to analyze the relationship between the part deformation, loads, and contact area for rivet-joint parts; the micro-deformation values for different stages are solved and obtained through theoretical analysis. According to the self-similarity of fractal theory model, the change of the micro-convex body for contact surface will be researched to reflect the macro-deformation properties. Through the measuring experiment for thin-wall parts, the actual three-dimensional coordinate value of each measuring point is obtained before and after riveting assembly, and then, the wavelet neural network method (WNNM) is adopted to predict experiment deformation value based on the obtained deformation value after processing the coordinate value through fitting surface method. Hereby, according to the deformation value for every thin-wall part after processing experiment data, the fractal dimension value will be determined based on the fractal statistic method to analyze the deformation status of different stages. Through analysis and comparison, the results show that the variation regularity of deformation value based on two or three fractal deformation stages is well conformed to and similar to the experimental value and prediction value, which also verify the correctness and effectiveness of the theoretical model, and provide a theoretical basis for further research on thin-wall part assembly deformation from a micro-perspective and improving assembly accuracy quality in future.

Crash and Trough Prediction: Fractal Theory Modeling for Hang Seng Index

This research is about the application of Fractal Theory and Power Law Model to predict the possible crash of the stock market in a bubble. The stock market used in this research is the Hong Kong stock market, i.e. the Hang Seng Index. The research found strong power of the Fractal Theory and Power Law Model in predicting the possible crash of the market.This could be a good starting paper of employing Fractal Theory and Power Law Model to other investment vehicle such as commodity, gold, energy, and currency in Hong Kong.