Implicit 3D Modeling of Ore Body from Geological Boreholes Data Using Hermite Radial Basis Functions

Wang, Jinmiao; Zhao, Hui; Bi, Lin; Wang, Liguan

doi:10.3390/min8100443

Cited by 25 publications

(10 citation statements)

References 30 publications

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“…Digital terrain models (DTMs) represent continuous terrain surfaces constructed using geological surveys and have been widely applied in various areas including min-ing engineering (Wang et al 2018), climate science (Hutchinson 1995) and geological modelling (Hillier et al 2014). It is also referred to as a digital elevation model or digital height model and their distinctions were discussed in (Li et al 2004).…”

Section: Introductionmentioning

confidence: 99%

Error indicators and adaptive refinement of the discrete thin plate spline smoother

Fang¹

2019

ANZIAMJ

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The discrete thin plate spline is a data fitting and smoothing technique for large datasets. Current research only uses uniform grids for this discrete smoother, which may require a fine grid to achieve a certain accuracy. This leads to a large system of equations and high computational costs. Adaptive refinement adapts the precision of the solution to reduce computational costs by refining only in sensitive regions. The error indicator is an essential part of the adaptive refinement as it identifies whether certain regions should be refined. Error indicators are well researched in the finite element method, but they might not work for the discrete smoother as data may be perturbed by noise and not uniformly distributed. Two error indicators are presented: one computes errors by solving an auxiliary problem and the other uses the bounds of the finite element error. Their performances are evaluated and compared with 2D model problems. References H. Chui and A. Rangarajan. A new point matching algorithm for non-rigid registration. Comput. Vis. Image Und., 89 (23): 114141, 2003. doi:10.1016/S1077-3142(03)00009-2. W. F. Mitchell. A comparison of adaptive refinement techniques for elliptic problems. ACM T. Math. Software, 15 (4): 326347, 1989. doi:10.1145/76909.76912. S. Roberts, M. Hegland, and I. Altas. Approximation of a thin plate spline smoother using continuous piecewise polynomial functions. SIAM J. Numer. Anal., 41(1):208234, 2003. doi:10.1137/S0036142901383296. G. Sewell. Analysis of a finite element method. Springer-Verlag, 1985. doi:10.1007/978-1-4684-6331-6. R. Sprengel, K. Rohr, and H. S. Stiehl. Thin-plate spline approximation for image registration. In P. IEEE EMBS, volume 3, pages 11901191. IEEE, 1996. doi:10.1109/IEMBS.1996.652767. L. Stals. Efficient solution techniques for a finite element thin plate spline formulation. J. Sci. Comput., 63(2):374409, 2015. doi:10.1007/s10915-014-9898-x. G. Wahba. Spline models for observational data, volume 59 of CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, 1990. doi:10.1137/1.9781611970128.

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Section: Introductionmentioning

confidence: 99%

Error indicators and adaptive refinement of the discrete thin plate spline smoother

Fang¹

2019

ANZIAMJ

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“…Guo et al (2016); Guo et al (2018); Guo et al (2020); Guo et al (2021) proposed an explicitimplicit-integrated 3D geological modelling approach for the geometric fusion of different types of complex geological structure models; therein, the HRBF-based implicit method was used to model general strata, faults, and folds, and the skinning method and the free-form surface were used to model local detailed structures. Wang et al (2018) proposed an implicit modeling approach to automatically build a 3D model for orebodies by means of spatial HRBF interpolation directly based on geological borehole data. However, the above RBF or HRBF interpolants, which use only the on-contact point datasets for each geological interface or assign an approximate gradient vector for each on-contact point according to its nearest attitude measurements, cannot be accurately consistent with actual attitude survey data.…”

Section: Related Workmentioning

confidence: 99%

AdaHRBF v1.0: Gradient-Adaptive Hermite-Birkhoff Radial Basis Function Interpolants for Three-dimensional Stratigraphic Implicit Modeling

Zhang

Khan

et al. 2023

Preprint

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Abstract. Three-dimensional (3D) stratigraphic modelling is capable of modeling the shape, topology, and other properties of strata in a digitalized manner. The implicit modeling approach is becoming the mainstream approach for 3D stratigraphic modelling, which incorporates both the off-contact attitudes and the on-contact occurrence information of stratigraphic interface to estimate the stratigraphic potential field (SPF) to represent the 3D architectures of strata. However, the magnitudes of SPF gradient controlling variation trend of SPF values cannot be directly derived from the known stratigraphic attribute or attitude data. In this paper, we propose an Hermite-Birkhoff radial basis function (HRBF) formulation, AdaHRBF, with an adaptive gradient magnitude for continuous 3D SPF modeling of multiple stratigraphic interfaces. In the linear system of HRBF interpolant constrained by the scattered on-contact attribute points and off-contact attitude points of a set of strata in 3D space, we add a novel optimizing term to iteratively obtain the true gradient magnitude. The case study shows that the HRBF interpolants can consistently establish accurate multiple stratigraphic interfaces and fully express the internal stratigraphic attribute and attitude. To ensure harmony of the variation of stratigraphic thickness, we adopt the relative burial depth of stratigraphic interface to the Quaternary as the SPF attribute value and propose a new stratigraphical thickness index (STI) to represent the variation trend of stratigraphic thickness in SPF. In addition, the proposed stratigraphic potential field modeling by HRBF interpolants can provide a suitable basic model for subsequent geosciences numerical simulation.

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“…Complete industrial ring networks and wireless networks covering entire mines have enabled the timely transmission of information and data [23,24]. The innovation of 3D modeling technologies can accurately model the ore body [25,26]. Remote management and control platforms have laid a good foundation for the remote production and operation of mines.…”

Section: Driving Force Of Reformmentioning

confidence: 99%

A New Reform of Mining Production and Management Modes under Industry 4.0: Cloud Mining Mode

Wang

et al. 2022

Applied Sciences

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In the context of Industry 4.0, using a new generation of information technology to activate and transform traditional industries will maintain the long-term competitiveness of traditional industries. The mining industry is also going through the process of informatization transformation. Through a literature survey, we analyze the current situation and challenges faced by mine production and operation management. Many mining companies are expanding in scale, but their operation and management methods are inefficient, and their business processes and organizational management methods need to be reformed. We propose a new mode named CM mode (cloud mining mode). We define this as integrating the core business of the mine (such as production and operation management, mining technology, planning services, etc.) into the cloud through effective use of cloud technologies, cloud resources, and cloud services. A large number of human and intellectual resources move to the cloud. A new mode of operation and management of mining industry clusters is thus formed; it is open, cooperative, and coordinated. We present five elements of the CM mode: data resources, digital technologies, digital talents, cloud business form, and cloud cooperation mode. We establish a “cloud–edge–terminal” technical framework of the CM mode, and describe its technical characteristics. We also describe three main application scenarios of the CM mode, and highlight the development path and key points of construction. The CM mode highlights a new development direction for the production and management of intelligent mines, and is of great significance for giving full play to the value of intelligent construction.

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Implicit 3D Modeling of Ore Body from Geological Boreholes Data Using Hermite Radial Basis Functions

Cited by 25 publications

References 30 publications

Error indicators and adaptive refinement of the discrete thin plate spline smoother

Error indicators and adaptive refinement of the discrete thin plate spline smoother

AdaHRBF v1.0: Gradient-Adaptive Hermite-Birkhoff Radial Basis Function Interpolants for Three-dimensional Stratigraphic Implicit Modeling

A New Reform of Mining Production and Management Modes under Industry 4.0: Cloud Mining Mode

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