A novel deep displacement sensor based on the electromagnetic induction theory is investigated and designed, which can directly convert the varied sliding displacement and tilt angle at any depth within the landslide mass to the variation of mutual inductance, so it has advantages, such as simple sensor structure, high sensitivity, accurate positioning of sliding surface and position, a remote, as well as real-time and automatic monitoring toward the underground landslide mass over the conventional deep displacement monitoring methods. The structure design, sensing principle, and theory modeling for the proposed sensor are presented. In order to improve the sensor's performance, the complicated relationship between the landslide mass's sliding magnitude and direction, the sensor's geometric parameters, and its corresponding mutual inductance were derived by theoretical modeling. Furthermore, a series of ground-based testing experiments and theoretical modeling simulation are conducted and compared in detail, which not only initially shows the design feasibility and modeling effectiveness for the proposed sensor, but is also useful to give an in-depth understanding of the sensor property and optimize the sensor design.

Deep displacement observation is one basic means of landslide dynamic study and early warning monitoring and a key part of engineering geological investigation. In our previous work, we proposed a novel electromagnetic induction-based deep displacement sensor (I-type) to predict deep horizontal displacement and a theoretical model called equation-based equivalent loop approach (EELA) to describe its sensing characters. However in many landslide and related geological engineering cases, both horizontal displacement and vertical displacement vary apparently and dynamically so both may require monitoring. In this study, a II-type deep displacement sensor is designed by revising our I-type sensor to simultaneously monitor the deep horizontal displacement and vertical displacement variations at different depths within a sliding mass. Meanwhile, a new theoretical modeling called the numerical integration-based equivalent loop approach (NIELA) has been proposed to quantitatively depict II-type sensors’ mutual inductance properties with respect to predicted horizontal displacements and vertical displacements. After detailed examinations and comparative studies between measured mutual inductance voltage, NIELA-based mutual inductance and EELA-based mutual inductance, NIELA has verified to be an effective and quite accurate analytic model for characterization of II-type sensors. The NIELA model is widely applicable for II-type sensors’ monitoring on all kinds of landslides and other related geohazards with satisfactory estimation accuracy and calculation efficiency.

Landslide is a very common and destructive geo-hazard, and displacement monitoring of it is integral for risk assessment and engineering prevention. Given the shortcomings of current landslide displacement monitor technologies, a new three-dimensional underground displacement monitoring technology is proposed based on the double mutual inductance voltage contour method. The underground displacement measuring device mainly consists of an information processing unit and sensing array, connected by power and RS-485 communication lines. An underground displacement measurement model to convert the double mutual inductance voltages and the inter-axis angle into the relative displacement between adjacent sensing units is established based on the interval-interpolation and contour-modeling. Under the control of the information processing unit, the relative displacement between any two adjacent sensing units can be calculated through the underground displacement measurement model, so as to obtain the total displacement from underground depth to surface, and the measurement data can be further sent to the Internet of things cloud platform through the 4G module; thus the remote real-time monitoring of underground displacement three-dimensional measurement for the rock and soil mass from underground depth to the surface is realized. The measurement model is verified by building an experimental platform to simulate the underground displacement of rock and soil mass. The experimental results show that for each measuring unit, when the horizontal displacement and vertical displacement are within the measurement range of 0–50 mm, the maximum measurement error will not exceed 1 mm, which can meet the accuracy requirements of underground displacement monitoring of landslide.

Deep displacement monitoring of rock and soil mass is the focus of current geological hazard research. In the previous works, we proposed a geophysical deep displacement characteristic information detection method by implanting magneto-electric sensing arrays in boreholes, and preliminarily designed the sensor prototype and algorithm of deep displacement three-dimensional (3D) measurement. On this basis, we optimized the structure of the sensing unit through 3D printing and other technologies, and improved the shape and material parameters of the permanent magnet after extensive experiments. Through in-depth analysis of the experimental data, based on the data query algorithm and the polynomial least square curve fitting theory, a new mathematical model for 3D measurement of deep displacement has been proposed. By virtue of it, the output values of mutual inductance voltage, Hall voltage and tilt measuring voltage measured by the sensing units can be converted into the variations of relative horizontal displacement, vertical displacement and axial tilt angle between any two adjacent sensing units in real time, and the measuring errors of horizontal and vertical displacement are tested to be 0-1.5 mm. The combination of structural optimization and measurement method upgrading extends the measurement range of the sensing unit from 0-30 mm to 0-50 mm. It shows that our revised deep displacement 3D measuring sensor can better meet the needs of high-precision monitoring at the initial stage of rock and soil deformation and large deformation monitoring at the rapid change and imminent-sliding stage. stage is characterized by cracks in the surface layer of rock and soil mass, followed by collapse [9]. Therefore, studying the deep displacement of rock and soil mass is more in line with the needs of disaster prevention and mitigation than the study of surface displacement. The deep displacement of rock and soil mass can reflect the dynamic stability of rock and soil mass more accurately and quickly, therefore it provides accurate, powerful data and theoretical support for early warning of landslides.However, the deep displacement measuring device must be buried deep underground, requiring the instrument to be strong, anticorrosive, convenient for installation, operation, long-distance signal transmission and so on. At the same time, the deep displacement monitoring environment is harsh and complicated, and there are problems such as no light, water seepage, corrosion, geotechnical shearing and extrusion, which can easily cause damage to the buried instruments. Therefore, compared with surface displacement monitoring, the development of deep displacement monitoring technology is relatively slow, and the types of deep displacement monitoring instruments that can be practically applied are obviously less and have poorer performance. At present, the global monitoring of deep displacement of rock and soil mass mainly includes borehole inclinometer, time domain reflection technology, Brillouin Optical Time Domain Reflection (BO...

The two-archive 2 algorithm (Two_Arch2) is a manyobjective evolutionary algorithm for balancing the convergence, diversity, and complexity using diversity archive (DA) and convergence archive (CA). However, the individuals in DA are selected based on the traditional Pareto dominance which decreases the selection pressure in the high-dimensional problems. The traditional algorithm even cannot converge due to the weak selection pressure. Meanwhile, Two_Arch2 adopts DA as the output of the algorithm which is hard to maintain diversity and coverage of the final solutions synchronously and increase the complexity of the algorithm. To increase the evolutionary pressure of the algorithm and improve distribution and convergence of the final solutions, an -domination based Two_Arch2 algorithm ( -Two_Arch2) for many-objective problems (MaOPs) is proposed in this paper. In -Two_Arch2, to decrease the computational complexity and speed up the convergence, a novel evolutionary framework with a fast update strategy is proposed; to increase the selection pressure, -domination is assigned to update the individuals in DA; to guarantee the uniform distribution of the solution, a boundary protection strategy based on indicator is designated as two steps selection strategies to update individuals in CA. To evaluate the performance of the proposed algorithm, a series of benchmark functions with different numbers of objectives is solved. The results demonstrate that the proposed method is competitive with the state-of-the-art multi-objective evolutionary algorithms and the efficiency of the algorithm is significantly improved compared with Two_Arch2.

Underground displacement monitoring is an effective method to explore deep into rock and soil masses for execution of subsurface displacement measurements. It is not only an important means of geological hazards prediction and forecasting, but also a forefront, hot and sophisticated subject in current geological disaster monitoring. In previous research, the authors had designed a novel electromagnetic underground horizontal displacement sensor (called the H-type sensor) by combining basic electromagnetic induction principles with modern sensing techniques and established a mutual voltage measurement theoretical model called the Equation-based Equivalent Loop Approach (EELA). Based on that work, this paper presents an underground displacement inversion approach named “EELA forward modeling-approximate inversion method”. Combining the EELA forward simulation approach with the approximate optimization inversion theory, it can deduce the underground horizontal displacement through parameter inversion of the H-type sensor. Comprehensive and comparative studies have been conducted between the experimentally measured and theoretically inversed values of horizontal displacement under counterpart conditions. The results show when the measured horizontal displacements are in the 0–100 mm range, the horizontal displacement inversion discrepancy is generally tested to be less than 3 mm under varied tilt angles and initial axial distances conditions, which indicates that our proposed parameter inversion method can predict underground horizontal displacement measurements effectively and robustly for the H-type sensor and the technique is applicable for practical geo-engineering applications.

Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation is proposed in this paper to improve the efficiency and accuracy of electromagnetic calculation. An image boundary extraction algorithm is developed to map the image on the geometric domain. Identification algorithm for the location of nodes in polygon area is proposed to determine the state of the node. To promote the average quality of the mesh and the efficiency of mesh generation, a novel force-based mesh smoothing algorithm is proposed. One test case and a typical electromagnetic calculation are used to testify the effectiveness and efficiency of the proposed algorithm. The results demonstrate that the proposed algorithm can produce a high-quality mesh with less iteration.

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