Random Midpoint Displacement Method Research Articles

Recovering 3D Basin Basement Relief Using High‐Precision Magnetic Data Through Random Forest Regression Algorithm: A Case Study of Tianzhen‐Yanggao Sag in Datong Basin

AbstractInversion of magnetic basement interfaces in basins is essential for interpreting potential field data and studying geothermal resource distribution, as well as basin formation and evolution. This paper introduces a novel method for inverting magnetic basement interfaces using a random forest regression (RFR) algorithm that combines potential field processing and machine learning techniques. The method creates magnetic base interface models and corresponding magnetic anomaly data through the random midpoint displacement method and magnetic interface finite element forward simulation. These anomalies are then processed using techniques such as directional transformations, analytical continuation, spatial derivatives, and fractional transformations. Feature attributes are extracted, and Gini importance is utilized to measure the contributions of feature factors, identify effective features, and enhance algorithm efficiency. The validity and practicality of the method are demonstrated through the analysis of both idealized and noisy models. The proposed machine learning‐based approach is more intelligent, efficient, and accurately represents the relief of magnetic base interfaces. When applied to magnetic survey data in the Datong Basin, it produced a reliable basin base model that aligns with known structural information, paving the way for further research in magnetic interface inversion.

Assembly accuracy analysis and phase optimization of aero-engine multistage rotors considering surface morphology and non-uniform contact deformation

The assembly accuracy of multistage rotors is crucial to guarantee the quality and performance of aero engines. However, traditional assembly accuracy analysis methods usually oversimplify geometric deviations as the degrees of freedom (DOF) variations relative to the ideal position, ignoring real surface morphology and the resulting non-uniform contact deformation. Therefore, this paper proposes an assembly accuracy analysis method that integrates the effects of surface morphology and non-uniform contact deformation on error propagation process, and further adopts a phase optimization method to improve the assembly accuracy of multistage rotors. Specifically, the surface morphology of rotor end faces is generated using the random midpoint displacement method. The Conjugate Gradient-Fast Fourier Transform (CG-FFT) algorithm is employed to calculate the non-uniform contact deformation. According to the simulation results, a fitting deformation surface (FDS) is constructed to determine the assembly position and orientation. On this basis, a novel error propagation model is established and the mounting phase of each stage rotor is optimized by a genetic algorithm (GA). A case study of a specific rotor system is carried out to verify the proposed error propagation model and give the optimized assembly combination with the objective of minimum coaxiality. This research effectively improves the prediction and actual assembly accuracy of aero-engine multistage rotors and provide a theoretical basis for the precision assembly of multistage rotors in aero-engine applications.

Recovering 3D Basement Relief Using Gravity Data Through Convolutional Neural Networks

AbstractGravity surveys in regional geophysical research can be used to estimate the depth of the sediment‐basement interface. In this study, we investigate a novel method using the convolutional neural network (CNN) for depth‐to‐basement inversion directly from gravity data. Based on the Random‐Midpoint‐Displacement method (RMD) and the features of the observed gravity data, we can generate a large set of realistic sediment‐basement interface models. This new method for model generation can significantly reduce the size of the training data sets which is usually considerably large to train a pervasive network. The application on synthetic models shows that the developed CNN inversion is able to capture the detailed features of the sediment‐basement interface for the complex geological model. However, so far, the training set obtained from the proposed method is still continuous and the CNN inversion still cannot effectively recover the models such as abrupt faults. We also successfully applied the developed method and workflow to a field study. The proposed approach opens a new window for estimating the physical contrast interfaces using potential field.

Development of a New Method for the Quantitative Generation of an Artificial Joint Specimen with Specific Geometric Properties

A rock joint is a planar discontinuity that has significant influence on the mechanical and hydraulic characteristics of rock mass. Laboratory experiments are often conducted on a joint to investigate and provide fundamental information for rock mass analysis. Although joint roughness and mechanical aperture exert great effects on the experimental results, controlling them in quantitative manner is quite complicated and consumptive in terms of specimen preparation. A new and simple method for the quantitative generation of the joint specimen was proposed in this study. Based on random midpoint displacement method, a joint specimen with a void space inside was generated. Parametric studies for the roughness and mechanical aperture were carried out, and as a result, the two joint properties could be controlled by manipulating input parameters of random midpoint displacement method. In order to validate the proposed method, two joint specimens, which had different levels of roughness and aperture, were generated and printed. Surface coordinates of the specimens were obtained by a 3D laser scanner, and calculated to make a comparison between the target values and the estimated values. Results showed that the method was capable of generating joint specimens with satisfactory precision.

랜덤중점변위법에 의한 거칠기의 생성 및 활용에 관한 연구

Quantification of roughness plays an important role in modeling strength deformability and fluid flow behaviors of rock joints. A procedure was suggested to simulate joint roughness, and characteristics of the roughness was investigated in this study. Stationary fractional Brownian profiles with known input values of the fractal parameter and other profile properties were generated based on random midpoint displacement method. Also, a procedure to simulate three dimensional roughness surface was suggested using the random midpoint displacement method. Selected statistical roughness parameters were calculated for the generated self-affine profiles to investigate the attribute of roughness. Obtained results show that statistical parameters applied in this study were able to consider correlation structure and amplitude of the profiles. However, effect of data density should be tackled to use statistical parameters for roughness quantification.

프랙탈 기법을 이용한 자연지형의 고도 복원

자연지형의 3D 디지털 지형모델(DTM)을 다루면서 소실된 셀의 데이터를 복원하거나, 저해상도의 DTM 이미지 일부를 컴퓨터 화면상에 확대표시 할 경우에는 존재하지 않는 데이터를 인위적으로 만들어줄 필요가 있다. 기존의 Bilinear법과 Bicubic법은 고도가 완만한 모델에는 잘 맞지만, 자연지형과 같이 무한의 상세함이 내재된 곳에는 부적합하다. 따라서 본 연구에서는 프랙탈 이론(Fractal theory)에 기초하여 자연지형을 보간하는 문제를 다루면서, 보간 전후 지형의 지형정보(프랙탈 차원과 표준편차)가 유지되는 한 방법을 제안한다. 이를 위해 DTM을 다수의 패치로 분할하고 프랙탈 기법으로 지형정보를 추출하고, 이 정보와 원래의 고도와 Random midpoint displacement법으로 보간한다. 제안된 알고리즘의 유효성을 확인하기 위해 가상의 프랙탈 지형을 만들어 시뮬레이션을 실시하고 기존의 방법과 비교한다. In this paper, we presents an algorithm which restores lost data or increases resolution of a DTM(Digital terrain model) using fractal theory. Terrain information(fractal dimension and standard deviation) around the patch to be restored is extracted and then with this information and original data, the elevations of cells are interpolated using the random midpoint displacement method. The results of the proposed algorithm are compared with those of the bilinear and bicubic methods on a fractal terrain map.

CONSTRUCTING CROSSOVER-FRACTALS USING INTRINSIC MODE FUNCTIONS

Real nonstationary time sequences are in general not monofractals. That is, they cannot be characterized by a single value of fractal dimension. It has been shown that many real-time sequences are crossover-fractals: sequences with two fractal dimensions — one for the short and the other for long ranges. Here, we use the empirical mode decomposition (EMD) to decompose monofractals into several intrinsic mode functions (IMFs) and then use partial sums of the IMFs decomposed from two monofractals to construct crossover-fractals. The scale-dependent fractal dimensions of these crossover-fractals are checked by the inverse random midpoint displacement method (IRMD).

Characterisation of the Soil Structure and Microwave Backscattering Based on Numerical Three-Dimensional Surface Representation: Analysis with a Fractional Brownian Model

In this paper, local structure of bare soil is analyzed from the fractal point of view. Soil surface profiles were created from three dimensional (3-D) stereoscopic images of soil surface leading to 3-D numerical reconstruction of the soil topography with very fine resolution. Investigations are done with a database (four soils) that includes three main soil classes according to the way of tillage: smoothed field from rainfalls, ploughed, and sowed fields. The fractional Brownian model developed by Mandelbrot is used to describe local structure of soil roughness. For the database soils, fractal nature of the profiles is demonstrated over a finite range of scales showing a good stability of fractal dimension for each one. This model also provides an excellent analytic fit to the experimental correlation function of soil. Therefore, a new method to calculate its shape at the origin and a more stable correlation length is presented. To study the influence of the band-limited fractal nature of the soil on radar signal, the Moment Method is used to evaluate the backscattered field and to obtain the radar cross-section by statistical averaging. Surfaces used for this electromagnetic simulation are cylindrical and perfectly conducting. A method is developed to generate soil surface profiles that have the same statistical properties and the same roughness parameters values (rms height, correlation length, and fractal dimension) as what has been found on our database soils. The generation method is based on an initially Gaussian correlated random profile, modified by the random midpoint displacement method to introduce the short-range disorder that depends on fractal dimension. The radar signal level computed on these surfaces by the Moment Method shows the dependence of backscattering on fractal dimension and new aspects in electromagnetic scattering behavior over soils.

Characteristics of surface roughening during plane strain compression of polycrystalline iron

Roughening behavior of the free surface of polycrystalline iron during plane strain compression is investigated experimentally. The changes in the shape of the free surface, which is roughened during plastic deformation, are observed in the three-dimensions. It is found that the mountains and the valleys of the roughened shape tend to elongate in the constrained direction for the specimen with isotropic grain shape. The shapes of the roughness curves in the loading direction and in the constrained direction are compared. The normalized height distribution of the roughness curve in the constrained direction is symmetric, while that of the roughness curve in the loading direction is asymmetric and positively skew during plane strain compression. Based on a simple simulation of the roughness curves by a random midpoint displacement method, this difference is supposed to be caused by the constraint of the material flow under plane strain condition.