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As a key component of remote-sensing technology, satellite gravity observation offers extensive coverage and high accuracy, effectively compensating for the shortcomings of terrestrial gravity measurements. Three-dimensional gravity data inversion can predict the physical property and spatial distribution of geological formations beneath the surface by analyzing the gravity data. In this paper, the heat source position within the Gonghe Basin’s geothermal system is identified through the analysis of satellite gravity data, and a constrained deep-learning inversion method is proposed. This method adds the fitting data constraints and depth-weighting function into the network model establishment of deep learning, and trains the network through a large number of datasets, so that the network is constrained by physical information in the training process to obtain the results with a better data-fitting accuracy and higher depth resolution. The proposed method is employed to verify the synthetic model data, and the inversion results indicated that, compared to other methods, the deep-learning gravity inversion method with the addition of physical information constraints has a higher inversion accuracy and depth resolution. Finally, the inversion results based on satellite gravity data revealed the presence of numerous low-density bodies in the underground range of 10–35 km in the research area. It is speculated that this part could be the heat source of the geothermal system in the Gonghe Basin. The findings from this study are expected to contribute to a deeper comprehension of the formation of the geothermal system in the region.

In an isolate-free graph G, a subset S of vertices is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number of G, denoted by $\\gamma _{t2}(G)$ , is the minimum cardinality of a semitotal dominating set in G. Using edge weighting functions on semitotal dominating sets, we prove that if $G\\neq N_2$ is a connected claw-free graph of order $n\\geq 6$ with minimum degree $\\delta (G)\\geq 3$ , then $\\gamma _{t2}(G)\\leq \\frac{4}{11}n$ and this bound is sharp, disproving the conjecture proposed by Zhu et al. [‘Semitotal domination in claw-free cubic graphs’, Graphs Combin. 33(5) (2017), 1119–1130].

The scanner is an important unit of the Coherent Doppler wind Lidar (CDWL) for long range detection. In the compact telescope system, a prism wedge rotating around the optical axis is often added to realize conical scanning of the laser beam. For the focused CDWL, the prism wedge can produce astigmatism in the measuring light, which will change the energy distribution in the detection space. Based on the geometric optics technique, the relation between the wedge parameters and the beam propagation status is analyzed in this paper. A modified range weighting function is also constructed by using the collection efficiency mode. A CDWL with 100 m focused distance was employed in the wind measurement experiments. Compared the measurement data from the CDWL with the anemometer at 50 m and 100 m height at the wind tower, the result indicates that the CDWL detection data is closer to the wind field at 50 m height, which is consistent with theoretical analysis. The optimized wedge parameters and the modified range weighting function are helpful for the further development of the miniaturized and lightweight CDWL.

A passive microwave instrument will be carried by China’s geostationary microwave satellite. A microwave hyper-spectral band included by the instrument ranges from 52.6 to 57.3 GHz, and totally has 89 channels in this spectral domain. The design of the hyper-spectral band is described from the aspects of scientific objectives and specifications. The weighting functions for each channel are calculated utilizing radiative transfer simulations under clear sky conditions. Then, the information content as well as the degree of freedom for signal are computed and analyzed to characterize this hyper-spectral sounding for atmospheric temperature profiling. Both the vertical distribution of the weighting functions and the width of retrieval averaging kernels indicate that the hyper-spectral band can provide more denser sampling for atmospheric temperature. The information content for the hyper-spectral band is approximately 46% higher than that of the ATMS-type channel 3 to 15, indicating that hyper-spectral measurement can improve the accuracy of retrieval. The most informative channels mainly locate near 57 GHz, having good consistency with the existing channels. The height range where the retrieval using the hyper-spectral observations is sensitive to the true profile, begins from about 800 to 1 hPa. Some channels can be considered as alternatives to each other since they have very similar information content and weighting functions. These results are expected to provide a valuable reference for future applications of the microwave hyper-spectral measurements.

A popular rule of thumb, usually called “heuristic technique” in Behavioral Economics, for determining the likelihood insensitivity regions of probability weighting functions (pwf’s) is based on searching for points at which the pwf’s are twice their values at half the points. Although this technique works remarkably well for many commonly used pwf’s, it sometimes fails to provide the correct answer. In order to cover the class of pwf’s for which the heuristic technique does not work, in this paper we propose, discuss, and illustrate an extension of the technique into what we call the “slicing method,” which is capable of finding the subadditivity and insensitivity regions of any continuous pwf.

Underground 3D density variation can be obtained via the inversion of gravity data, which is a very important basis for structural division, oil and gas structure definition, and mineral resource evaluation. A depth-weighting function is usually introduced as a structural constraint in density inversion to solve the skin effect. We propose an adaptive space–location-weighting (ASW) function for gravity field data to improve the resolution of the inversion, which adds the position and depth information provided by the DEXP method to form a new weighting function. The weighting function is partitioned according to the horizontal distribution of the source and can effectively improve the resolution of field sources with different positions and different depths. The results of model tests have shown that the ASW function method can significantly improve the precision and resolution of density inversion results and has good noise immunity. The ASW method was applied to interpret the real gravity data of a mining area in Shandong, and we speculated potential mineralization based on the inversion results, which corresponded well with the logging results.

In this paper, an adaptive-weight model predictive control (AW-MPC) strategy is proposed to address the trajectory tracking problem of a lower-limb rehabilitation exoskeleton robot. First, based on human motion analysis, the dynamics of the lower-limb rehabilitation exoskeleton are established, and the nonlinear dynamic model is transformed into a linear model. Second, a MPC objective function is formulated to minimize the tracking error, yielding the optimal control input. Then, on the basis of conventional MPC, a weight-tuning scheme is developed: a weighting function is constructed according to the evolution of the tracking error to adaptively adjust the MPC weighting coefficients, and the closed-loop stability of the control system is proven via a Lyapunov-based analysis. Finally, the proposed method is validated on a lower-limb rehabilitation exoskeleton experimental platform, with a PID controller designed as a baseline for comparison. The experimental results demonstrate that, compared with the PID controller, the proposed AW-MPC achieves faster convergence of the tracking error, higher tracking accuracy, and enhanced robustness.

The demand for multiphase flow measurement is widespread in petrochemical and other fields. Due to its small size, easy maintenance, and no moving parts, electromagnetic flowmeters are widely used in single fluid measurement. With the increasing application of traditional electromagnetic flowmeters in petrochemical and other fields, the problems of traditional electromagnetic flowmeters in multiphase flow measurement applications have been discovered. How to optimize the structure of the electromagnetic flowmeter and how to improve the measurement accuracy has become a new research focus. On the basis of a large number of literature studies, this research is based on the finite element method, and systematically studies the influence of multiphase flow on the weight function of electromagnetic flowmeters. Firstly, modeling the existence of non-conductive objects in the electromagnetic flowmeter. Secondly, analyze the weight function characteristics of the non-conductive objects on the electromagnetic flowmeter from two angles of different radii and different positions. The conclusions of this study can provide a certain reference basis for the electromagnetic flowmeter in the measurement of multiphase flow.

Noise emitted by rolling tires has a strong contribution on the traffic noise in urban areas and has a significant impact on the ride comfort for passengers, which is mainly caused by the interaction between tires and pavement. The force generated in the contact patch has an important contribution to tire noise. For a patterned tire rolling on a flat surface, the geometry and position of tread pattern blocks are one of the main influencing factors of discontinuous force. In this paper, it is assumed that the impact force produced by each tread pattern element and pavement can be expressed as a Dirac delta function. For more realistic modelling of noise generated by impact force, a weighting function is considered, which is distributed along the tread transverse direction. The experiment is performed on a drum experimental machine in a semi-anechoic room. The predicted results are compared with experimental measurement, the maximum error is 3.85 dB between the predicted sound pressure level and measured. The prediction results have sufficient accuracy on the trend of A-weighted sound pressure level. The prediction method in this paper can be used to accelerate the development process of low tire tread pattern in the future.

The meshless displacement error-recovery parametric investigation in finite element method-based incompressible elastic analysis is presented in this study. It investigates key parameters such as interpolation schemes, patch configurations, dilation indexes, weight functions, and meshing patterns. The study evaluates error recovery effectiveness (local and global), convergence rates, and adaptive mesh improvement for triangular/quadrilateral discretization schemes. It uses meshless moving least squares (MLS) interpolation with rectangular and circular support regions and solves benchmark plate and cylinder problems. It is observed that a circular influence region, a cubic spline weight function, and regular mesh patterns yield a better performance of than an MLS-based error recovery method. The study also concludes that lower dilation index values with rectangular influence regions are preferable for regular meshes, while higher dilation index values with radial influence regions are suitable for preferable meshes to enhance MLS error recovery.