Integration of Information Theory, Fractal Theory and Statistical Analyses for Landslide Susceptibility Mapping at Regional Scales

A new model, integrating information theory, fractal theory and statistical model for accurate landslide susceptibility mapping (LSM) at regional scales, has been proposed. In this model, landslide conditional factors are firstly classified with an optimal number of classes, which is determined by maximizing their information coefficients estimated from Shannon’s entropy model. The spatial association between influencing factors and induced landslides has been measured by introducing the variable fractal dimension method (VFDM). The VFDM approach fully considers the characteristics of landslide fractal distribution. Then the fractal dimensions (\(D\)) are calculated to provide multiple factors with various numerical weights. The proposed model eventually combines the landslide frequency ratio (\(fr\)) of each factor with corresponding weight to achieve spatial prediction of landslides, illustrated by an example area in China. In the study area, 500 landslides have been identified by aerial photograph interpretation, extensive field investigations, historical and bibliographical landslide data. In the model, these landslides are randomly split into a training dataset (70 %)and a validating dataset (30 %) Seven factors are recognized and analyzed by frequency ratio (FR) method, including lithology, distance to fault, altitude, slope, aspect, distance to stream and distance to the road. The receiver operating characteristic curve (AUROC) has been adopted to compare and validate the model results. Results show that the proposed landslide model achieved a more accurate prediction with AUROC equal to 0.8467, over-performing than the conventional frequency ratio method (AUROC=0.8088). According to the final prognostic landslide susceptibility map, 16.37 % f the study area shows very high and high susceptibility, accounting for 63.55 % f the entire landslides. Evaluation of relative factor importance based on a one-by-one factor removal test indicates that the lithology factor contributes unique information for landslides. In conclusion, the example demonstrates that the proposed framework is promising for further improvement of LSM.

Normalized Ratcheting Diagram Under Sinusoidal Vibration Waves

Ratcheting is a progressive incremental inelastic deformation or strain which can occur in a component that is subjected to variations of mechanical stress, thermal stress, or both. This study concentrated on the ratcheting occurrence of the piping model under the combined effect of constant external force and dynamic cyclic vibrations. Bent solid bars represented piping models, and sinusoidal acceleration waves were loaded. Characteristics of seismic loads between load-controlled and displacement-controlled properties were studied from the viewpoint of the frequency ratio of the forcing frequency to the natural frequency of the piping model. Besides, the ratcheting occurrence conditions of the beam and the piping model were compared in one normalized diagram to display the general mechanism of ratcheting with the consideration of the effect from the difference of shape and material. Results show that ratcheting occurs easily with a lower frequency ratio in both beam and piping models. In addition, it is meaningful to use beam models to understand the ratcheting mechanism of piping models. Describing the occurrence of ratcheting using the normalized ratcheting diagram for different components is feasible.

A Study on Nonlinear Dynamic Response of the Large-Span Roof Structure with Suspended Substructure

Nowadays, it is common to see large public buildings, e.g., stadiums, with some equipment or substructure suspended from the center of the roof. These substructures will tend to be larger and heavier the more gear is needed, which may have negative impacts on the dynamic performance of the roof structures. In this paper, to explore the dynamic response of a large-span roof structure with a suspended substructure, a real structure model is simplified into a two-degrees-of-freedom system. The essential consideration of nonlinear vibration is elaborated in the equations of motions. Approximate analytical solutions for free and forced vibrations are derived using perturbation methods, while numerical analysis is carried out to validate the solutions. The ratio of linear to nonlinear amplitude is proposed to represent the nonlinear effect of the primary structure, and the nonlinear effect, varying with structural parameters of frequency ratio, mass ratio, excitation ratio, and external force to the primary structure, is investigated. It is shown that internal resonance occurs when the structural frequency ratio is close to 1:2 and that secondary resonance takes place due to certain external excitations; internal resonance and secondary resonance will magnify the amplitude of the primary structure during vibration. Finally, a case of a designed practical dome with a suspended substructure is studied to verify the outcomes from the above research. According to these findings, some design proposals for this type of structure are provided.

Hybrids of Support Vector Regression with Grey Wolf Optimizer and Firefly Algorithm for Spatial Prediction of Landslide Susceptibility

Landslides are one of the most frequent and important natural disasters in the world. The purpose of this study is to evaluate the landslide susceptibility in Zhenping County using a hybrid of support vector regression (SVR) with grey wolf optimizer (GWO) and firefly algorithm (FA) by frequency ratio (FR) preprocessed. Therefore, a landslide inventory composed of 140 landslides and 16 landslide conditioning factors is compiled as a landslide database. Among these landslides, 70% (98) landslides were randomly selected as the training dataset of the model, and the other landslides (42) were used to verify the model. The 16 landslide conditioning factors include elevation, slope, aspect, plan curvature, profile curvature, distance to faults, distance to rivers, distance to roads, sediment transport index (STI), stream power index (SPI), topographic wetness index (TWI), normalized difference vegetation index (NDVI), landslide, rainfall, soil and lithology. The conditioning factors selection and spatial correlation analysis were carried out by using the correlation attribute evaluation (CAE) method and the frequency ratio (FR) algorithm. The area under the receiver operating characteristic curve (AUROC) and kappa data of the training dataset and validation dataset are used to evaluate the prediction ability and the relationship between the advantages and disadvantages of landslide susceptibility maps. The results show that the SVR-GWO model (AUROC = 0.854) has the best performance in landslide spatial prediction, followed by the SVR-FA (AUROC = 0.838) and SVR models (AUROC = 0.818). The hybrid models of SVR-GWO and SVR-FA improve the performance of the single SVR model, and all three models have good prospects for regional-scale landslide spatial modeling.

Interval of restitution coefficient for chattering in impact damper

Based on the impact damper, a dynamic model of a non-fixed constrained collision system was established. The coefficient of restitution is used as the main control parameter to analyze the system’s periodic movement and its bifurcation region. The chattering movement characteristics of the system were revealed. The interval of restitution coefficient for the chattering of collision system under various mass ratio and frequency ratio was obtained. The results show that the chattering phenomenon occurs in the collision system when the coefficient of restitution is greater than 0.5; as the mass ratio decreases, the interval of restitution coefficient for chattering continues to expand; as the frequency increases, the interval of restitution coefficient for chattering narrows.

Frequency ratio application for mapping flood susceptibility in Welang Watershed, East Java

Flood is one of the disaster threats downstream of Welang river, Pasuruan. A flood susceptibility map is needed to anticipate floods disasters. This research aimed to map flood Susceptibility in the Welang watershed using a Geographical Information System. In determining flood hazard, the Frequency Ratio (FR) approach was used. Flood locations were identified from the interpretation of field survey data as training data and model validation. The data were represented in a Digital Elevation Model (DEM) map, geological data, land use, river data, and Landsat Satellite Imagery and processed into a spatial database on the GIS platform. The factors that caused flooding consisted of Flood inventory, slope, Elevation, Topographic Wetness Index (TWI), Standardized Precipitation Index (SPI), Flow Accumulation, Distance to the river, River Density, Rainfall, Vegetation Index (NDVI), and Landuse. The map results with acceptable accuracy showed that the FR model gained an Area Under Curve (AUC) value of 90%, and the incidence for the Area Under Curve ( AUC ) was 93%. It is known that 1% of the flood-prone area is very high. The local Government can use the research to minimize the risk of flooding in the Welang watershed.