Health monitoring of Bridges based on multifractal theory

The multifractal theory is applied in an analysis of bridge disturbance signals with the aim of investigating their nonlinear characteristics, and then the recognisable fault features are extracted from them. By calculating the box dimension and correlation dimension of the bridge disturbance signal, the dimensional characteristics of the disturbance data are analysed to distinguish the health-state of the bridge. Finally, taking the bridge disturbance data as an example, and by using the multifractal spectrum analysis of the disturbance data, it is concluded that the multifractal method can accurately identify the fault state and realise the bridge health monitoring.

Spatial distribution of soil water and salt in a slightly salinized farmland

It is important to study the mechanisms associated with the spatial distribution of soil water and salt to control soil salinization and promote the sustainable development of farmland. In this study, six plots in gully farmland in the loess hilly region with different spatial locations were selected to determine the spatial distributions of soil water and salt and their correlation using the multifractal method. A grid method (15 m  15 m, 3,600 m2) was applied in the 0–20 and 20–40 cm soil layers where each sampling site was located at the center point coordinates. The results showed that the spatial variability of the soil water and salt were 1.41 and 1.73 times higher, respectively, in the upstream farmland than the downstream farmland. The uneven runoff and sediment distributions from gullies in the upstream farmland increased the spatial variability of the soil water and salt. In addition, the vulnerability of upstream farmland to waterlogging caused further in their spatial variability due to narrow landform features. Analysis using the joint multifractal method showed that the spatial variability of the soil water and salt was strongly correlated (P < 0.05) because of the coupling between soil water and salt. In addition, the spatial variability of the soil water and salt was strongly correlated in the 0−20 and 20−40 cm layers because of the spatial autocorrelations of the soil properties (P < 0.05), thereby indicating that the spatial distributions of soil water and salt in the whole soil layer could be represented by those in the 0−20 cm layer. Thus, we recommend using the 0−20 soil layer to sample the distributions of the soil water and salt. Our results provide a theoretical basis for studying the interactive mechanisms associated with the distributions of soil water and salt, and for optimizing the sampling method in the study area.

Multifractal Analysis of Acoustic Emissions during Hydraulic Fracturing Experiments under Uniaxial Loading Conditions: A Niutitang Shale Example

Fracture characterization is essential for estimating the stimulated reservoir volume and guiding subsequent hydraulic fracturing stimulations in shale reservoirs. Laboratory fracturing experiments can help provide theoretical and technical guidance for field operations. In this study, hydraulic fracturing experiments on the shale samples from Niutitang Formation in Hunan Province (China) under a uniaxial loading condition are conducted. The multifractal method is used to analyze the acoustic emission (AE) signals and characterize fracture initiation and propagation. The hydraulic fracturing process can be divided into three stages based on the characteristics of AE signals: the initial stage, the quite stage, and the fracturing stage. The multifractal analysis results showed that: (1) the value of the spectrum width, Δα, continues to increase as the energy accumulates until the fracturing stage starts; and (2) the difference in the multifractal spectrum values, Δf, reflects the relationship between small and large signal frequencies and can quantify the fracture scale, i.e., the lower the Δf, the larger the fracture scale and vice versa. The results were further verified using a time-frequency analysis of the AE signals and micro-CT scanning of the samples. This study demonstrates that the multifractal method is feasible for quantitatively characterizing hydraulic fractures and can aid field hydraulic fracturing operations.

STUDY ON COAL FRACTOGRAPHY UNDER DYNAMIC IMPACT LOADING BASED ON MULTIFRACTAL METHOD

Coal fractography is a powerful tool for interpreting coal fracture behaviors, which is significant for dealing with failure issues encountered in deep coal mining. However, the accuracy of coal fractography highly depends on the method of quantitatively characterizing coal fracture surfaces. In this study, coal fractography under dynamic impact loading was investigated based on a multifractal method, the multifractal spectrum parameters were proposed to quantitatively describe the coal fracture surfaces. The width of the multifractal spectrum [Formula: see text] characterizes the uniformity of the surface asperity distribution, and the spectrum parameter [Formula: see text]–[Formula: see text] characterizes the proportion of dominant asperities on fracture surface. The coal fractography results indicate that larger loading rate leads to more asperities on the coal fracture surfaces, i.e. rougher fracture surfaces, and the fracture surfaces are dominated by small asperities induced by dynamic impact loading. In addition, significant anisotropy effect was found on the fracture surfaces under dynamic impact loading by the spatial distributions of multifractal spectrum parameter [Formula: see text]. The parameter [Formula: see text] was further utilized to determine the macrocrack direction and microfracture markings on the coal fracture surfaces, the results transpire that the multifractal method is feasible for coal fractographic analysis under dynamic loading conditions.

Выявление динамических закономерностей эпилептических приступов у детей методами нелинейной механики

Recurrence quantification analysis and multifractal method were used for investigation of the encephalogram time series of the children with epileptic seizures. It has been shown that epileptic seizures are accompanied by the increase in determinism of the brain electric process due to neuron activity synchronization. This behavior is similar to the catastrophic behavior in nonlinear systems of different nature