A Multidimensional Spatial Analysis System for Vanadium-Titanium Magnetite Based on Third-Order Tensor Decomposition

Abstract

This invention relates to the field of mineral exploration technology, and more particularly to a multidimensional spatial analysis system for vanadium-titanium magnetite based on third-order tensor decomposition. The system includes: a data acquisition module for acquiring vanadium-titanium magnetite core samples and third-order magnetic gradient tensor data; a mineralogical analysis module for determining the spatial distribution complexity and liberation degree of vanadium-titanium magnetite; a tensor decomposition module for calculating the internal structural complexity of vanadium-titanium magnetite at various sounding depths; a mapping relationship construction module for constructing a first mapping relationship between spatial distribution complexity and the liberation degree of vanadium-titanium magnetite, and a second mapping relationship between structural complexity and spatial distribution complexity; and a mineability assessment module for assessing the mineability of vanadium-titanium magnetite at different sounding depths. This invention combines in-well third-order magnetic gradient tensor detection technology with core mineralogical analysis technology, effectively improving the reliability of vanadium-titanium magnetite mineability assessment.

Description

Technical Field

[0001] This invention relates to the field of mineral exploration technology, and in particular to a multidimensional spatial analysis system for vanadium-titanium magnetite based on third-order tensor decomposition. Background Technology

[0002] Vanadium-titanium magnetite, as an important strategic mineral resource, is not only a basic raw material for the steel industry but also a major source of key rare metals such as vanadium and titanium. In the process of deep mineral exploration and resource evaluation, accurately locating ore bodies, revealing their internal structural characteristics, and predicting the usability of the ore are core challenges faced by geological exploration and mining engineering.

[0003] With the development of magnetic exploration instrument technology and signal processing theory, the increasing order of observed physical quantities has become a trend in the evolution of borehole magnetic surveying technology. The third-order magnetic gradient tensor contains multiple higher-order derivative components, which can describe more subtle changes in the magnetic field in space. Compared with traditional magnetic field data and low-order gradient data, it can further improve the ability to identify deep small-scale anomalies, complex boundary structures, and heterogeneous ore bodies.

[0004] Current technologies typically treat in-well magnetic observations and mineralogical analysis separately, failing to effectively establish a mapping relationship between macroscopic magnetic response characteristics and microscopic mineralogical properties. The mineability of vanadium-titanium magnetite depends not only on the macroscopic location of the ore body but also on the microscopic mineral embedding characteristics and the ease of liberation within the ore. Therefore, how to utilize the decomposition characteristics of the third-order magnetic gradient tensor to quantitatively characterize the spatial heterogeneity of vanadium-titanium magnetite in gangue, and further deduce its degree of liberation variation, to achieve rapid assessment of ore mineability at different well depths, is a technological gap that urgently needs to be filled in the current deep mineral resource exploration technology system. Summary of the Invention

[0005] To overcome the defects and shortcomings of existing technologies, this invention provides a multi-dimensional spatial analysis system for vanadium-titanium magnetite based on third-order tensor decomposition. By combining the third-order magnetic gradient tensor detection technology in wells with core mineralogical analysis technology, the reliability of the evaluation of the mineability of vanadium-titanium magnetite is effectively improved.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a multidimensional spatial analysis system for vanadium-titanium magnetite based on third-order tensor decomposition, comprising: The data acquisition module is used to acquire vanadium-titanium magnetite core samples from the target mining area and the third-order magnetic gradient tensor data at the corresponding depth sounding locations. The mineralogical analysis module is used to perform mineralogical analysis on vanadium-titanium magnetite core samples to determine the spatial distribution complexity of vanadium-titanium magnetite in gangue and the degree of liberation of vanadium-titanium magnetite. The degree of liberation of vanadium-titanium magnetite is the ratio of the number of liberated individual vanadium-titanium magnetite particles to the total number of mineral particles. The tensor decomposition module is used to decompose the third-order magnetic gradient tensor data, determine the tensor decomposition rank, weight distribution characteristics and directional distribution characteristics of the third-order magnetic gradient tensor, and calculate the structural complexity of the vanadium-titanium magnetite at each sounding location. The mapping relationship construction module is used to construct the first mapping relationship between spatial distribution complexity and the dissociation degree of vanadium-titanium magnetite, and the second mapping relationship between structural complexity and spatial distribution complexity. The mineability assessment module is used to assess the mineability of vanadium-titanium magnetite at different depth locations based on the internal structural complexity of the vanadium-titanium magnetite, combined with a first mapping relationship and a second mapping relationship.

[0007] Furthermore, the specific execution steps of the data acquisition module for acquiring third-order magnetic gradient tensor data include: acquiring magnetic field time-domain measurement signals at each depth measurement location of the well using a rotating magnetic sensor; performing a Fourier transform on the magnetic field time-domain measurement signals to obtain frequency-domain spectral data at the corresponding depth measurement locations, thus completing the conversion from time-domain signals to frequency-domain signals; extracting the corresponding magnetic gradient tensor components according to different frequency orders based on the frequency-domain spectral data, and recombining the components according to the arrangement rules of the third-order spatial derivative tensor to generate third-order magnetic gradient tensor data at each depth location.

[0008] Furthermore, the specific execution steps for determining the spatial distribution complexity of vanadium-titanium magnetite in gangue within the mineralogical analysis module include: Vanadium-titanium magnetite core samples were directionally cut, resin-mounted, progressively ground, and mirror-polished to prepare standard cross-section samples that meet the requirements of micromineralogical analysis. An automatic mineral parameter analysis system was used to perform scanning electron microscopy and energy dispersive spectroscopy on standard cross-section samples to generate mineral spatial distribution data including mineral type, particle centroid coordinates, particle boundary contours, and particle area. The standard cross-section sample is divided into different spatial statistical units according to the preset grid size, and the volume fraction of vanadium-titanium magnetite in each spatial statistical unit is calculated based on the mineral spatial distribution data. The volume fraction of vanadium-titanium magnetite in all spatial statistical units is statistically analyzed and the spatial variation coefficient is calculated. The spatial variation coefficient is used as the spatial distribution complexity of vanadium-titanium magnetite to characterize the non-uniform distribution of vanadium-titanium magnetite in gangue.

[0009] Furthermore, the specific execution steps for calculating the structural complexity inside the vanadium-titanium magnetite at each depth sounding location in the tensor decomposition module include: By decomposing the third-order magnetic gradient tensor data, tensor decomposition parameters at each sounding location are obtained. The tensor decomposition parameters include tensor decomposition rank, weighted discrete coefficients, and directional discrete coefficients. The decomposition process can be either CP decomposition or Tucker decomposition. Based on the distribution characteristics of the tensor decomposition parameters, the standardized contribution of each tensor decomposition parameter is determined, and the standardized contribution is used as a weight to perform a weighted summation of each tensor decomposition parameter to obtain the structural complexity of the vanadium-titanium magnetite at the corresponding sounding location.

[0010] Furthermore, the specific execution steps for determining the standardized contribution of each tensor decomposition parameter based on the distribution characteristics of the tensor decomposition parameters include: Statistical analysis of tensor decomposition parameters at all depth sounding locations in the target mining area; The standard deviations of each tensor decomposition parameter within the target mining area are calculated to characterize the sensitivity of the corresponding tensor decomposition parameters to the spatial differences of the ore body. The ratio of the standard deviation of each tensor decomposition parameter to the sum of the standard deviations of all tensor decomposition parameters is taken as the standardization contribution of the corresponding tensor decomposition parameter.

[0011] Furthermore, the specific execution steps of the mapping relationship construction module include: using the sounding location of the vanadium-titanium magnetite core sample as the calibration sounding location, extracting the spatial distribution complexity, dissociation degree, and structural complexity at the calibration sounding location, and constructing a calibration sample dataset; based on the calibration sample dataset, fitting the relationship between spatial distribution complexity and dissociation degree to establish a first mapping relationship between spatial distribution complexity and the dissociation degree of vanadium-titanium magnetite, used to characterize the influence law of changes in spatial distribution complexity on changes in dissociation degree; based on the calibration sample dataset, fitting the relationship between structural complexity and spatial distribution complexity to establish a second mapping relationship between structural complexity and spatial distribution complexity, used to characterize the correspondence between magnetic response structural characteristics and mineral spatial distribution state.

[0012] Furthermore, the specific executable steps of the exploitability assessment module include: The structural complexity of the vanadium-titanium magnetite at each sounding location is obtained, and the structural complexity is input into the second mapping relationship to obtain the predicted value of the spatial distribution complexity at the corresponding sounding location. Input the spatial distribution complexity prediction value into the first mapping relationship, and calculate the vanadium-titanium magnetite liberation degree prediction value at the corresponding sounding location; The exploitability evaluation index at each sounding location is obtained by weighted summing of the reciprocal of the structural complexity parameter, the reciprocal of the predicted spatial distribution complexity, and the predicted degree of liberation of vanadium-titanium magnetite at each sounding location. Locations with a exploitability evaluation index greater than the preset exploitability evaluation threshold are designated as priority mining areas, while locations with an exploitability evaluation index less than or equal to the preset exploitability evaluation threshold are designated as temporarily deferred mining areas.

[0013] Secondly, the present invention provides a multidimensional spatial analysis method for vanadium-titanium magnetite based on third-order tensor decomposition, comprising: Acquire vanadium-titanium magnetite core samples from the target mining area and the third-order magnetic gradient tensor data at the corresponding depth sounding locations; Mineralogical analysis was performed on vanadium-titanium magnetite core samples to determine the spatial distribution complexity of vanadium-titanium magnetite in gangue and the degree of vanadium-titanium magnetite liberation. The degree of vanadium-titanium magnetite liberation is the ratio of the number of liberated individual vanadium-titanium magnetite particles to the total number of mineral particles. The third-order magnetic gradient tensor data is decomposed to determine the tensor decomposition rank, weight distribution characteristics and directional distribution characteristics of the third-order magnetic gradient tensor, and the structural complexity of the vanadium-titanium magnetite at each sounding location is calculated. We construct a first mapping relationship between spatial distribution complexity and the dissociation degree of vanadium-titanium magnetite, and a second mapping relationship between structural complexity and spatial distribution complexity. Based on the structural complexity of the vanadium-titanium magnetite at each sounding location, combined with the first and second mapping relationships, the mineability of the vanadium-titanium magnetite at different sounding locations is assessed.

[0014] Thirdly, the present invention provides an electronic device, comprising: a processor and a memory, wherein the memory stores a computer program that can be called by the processor, and the processor executes a multidimensional spatial analysis method for vanadium-titanium magnetite based on third-order tensor decomposition by calling the computer program stored in the memory.

[0015] Fourthly, the present invention provides a computer-readable storage medium storing instructions that, when executed on a computer, cause the computer to perform a multidimensional spatial analysis method for vanadium-titanium magnetite based on third-order tensor decomposition.

[0016] Compared with the prior art, the present invention has the following advantages and beneficial effects: This invention combines in-well third-order magnetic gradient tensor probing technology with core mineralogical analysis. Leveraging the high sensitivity of the third-order magnetic gradient tensor to local magnetic response changes, and combining this with the decomposition rank, weight distribution characteristics, and directional distribution characteristics obtained from tensor decomposition, it can effectively characterize the complexity of the internal structure of ore bodies, achieving precise identification of spatial structural information of deep ore bodies. Simultaneously, by extracting spatial distribution complexity and liberation parameters from core samples and establishing a mapping relationship between structural complexity and mineralogical properties, geophysical response parameters can be directly correlated with the internal occurrence state of the ore, effectively improving the reliability of the assessment of the mineability of vanadium-titanium magnetite. Attached Figure Description

[0017] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a schematic diagram of the structure of a vanadium-titanium magnetite multidimensional spatial analysis system based on third-order tensor decomposition provided in an embodiment of the present invention; Figure 2 This is a flowchart illustrating a method for multidimensional spatial analysis of vanadium-titanium magnetite based on third-order tensor decomposition provided in an embodiment of the present invention. Figure 3 This is a schematic diagram of the structure of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0018] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0019] Please see Figure 1 , Figure 1This is a schematic diagram of a multidimensional spatial analysis system for vanadium-titanium magnetite based on third-order tensor decomposition provided in an embodiment of the present invention. It includes: a data acquisition module 110, used to acquire vanadium-titanium magnetite core samples from the target mining area and the third-order magnetic gradient tensor data at the corresponding depth sounding locations; a mineralogical analysis module 120, used to perform mineralogical analysis on the vanadium-titanium magnetite core samples to determine the spatial distribution complexity of vanadium-titanium magnetite in gangue and the degree of liberation of vanadium-titanium magnetite, where the degree of liberation is the ratio of the number of liberated individual vanadium-titanium magnetite particles to the total number of mineral particles; and a tensor decomposition module 130, used to analyze the third-order magnetic gradient tensor. The quantitative data is decomposed to determine the tensor decomposition rank, weight distribution characteristics, and directional distribution characteristics corresponding to the third-order magnetic gradient tensor, and the structural complexity of the vanadium-titanium magnetite at each sounding location is calculated. The mapping relationship construction module 140 is used to construct the first mapping relationship between spatial distribution complexity and the dissociation degree of vanadium-titanium magnetite, and the second mapping relationship between structural complexity and spatial distribution complexity. The mineability assessment module 150 is used to assess the mineability of vanadium-titanium magnetite at different sounding locations based on the structural complexity of the vanadium-titanium magnetite at each sounding location combined with the first and second mapping relationships.

[0020] In this embodiment of the invention, the data acquisition module 110 is used to acquire vanadium-titanium magnetite core samples from the target mining area and the third-order magnetic gradient tensor data at the corresponding depth sounding locations. The vanadium-titanium magnetite core samples are obtained through drilling operations using a core drilling rig in the target mining area. Acquiring the third-order magnetic gradient tensor data at the corresponding depth sounding locations includes: acquiring the magnetic field time-domain measurement signals at each depth sounding location of the drilling using a rotating magnetic sensor; performing a Fourier transform (FFT) on the magnetic field time-domain measurement signals, setting the number of sampling points for the Fourier transform to 1024 points, decomposing the time-domain signal into frequency-domain signals with different frequency components, and calculating... The amplitude and phase of each frequency component are used to obtain the frequency domain spectral data at the corresponding depth measurement location, completing the conversion from time domain signal to frequency domain signal. Based on the frequency domain spectral data, the corresponding magnetic gradient tensor components are extracted according to different frequency orders. That is, the characteristic spectral values ​​corresponding to the fundamental frequency component, second harmonic component and third harmonic component in the frequency domain spectral data are extracted, and the corresponding first-order gradient term, second-order gradient term and third-order gradient term are obtained respectively. The components are reorganized according to the arrangement rules of the third-order spatial derivative tensor (arranged along the third-order partial derivatives of the three spatial coordinate axes of x, y and z, a total of 27 components) to generate the third-order magnetic gradient tensor data at each depth location.

[0021] The spatial distribution complexity of vanadium-titanium magnetite in gangue refers to the uniformity of the spatial distribution of vanadium-titanium magnetite mineral particles in the gangue matrix. This is specifically quantified by the coefficient of spatial variation (CSP). A larger CSP indicates a more uneven distribution and stronger aggregation of vanadium-titanium magnetite in the gangue, while a smaller CSP indicates a more uniform distribution. Its core meaning is to reflect the spatial coexistence state of vanadium-titanium magnetite and gangue, directly related to the difficulty of ore crushing and gangue separation efficiency during subsequent mining. The degree of liberation of vanadium-titanium magnetite refers to the ratio of the number of liberated vanadium-titanium magnetite particles to the total number of mineral particles. Its core meaning is to reflect the ease with which vanadium-titanium magnetite particles are separated from the mineral. A higher degree of liberation indicates a greater number of individual vanadium-titanium magnetite particles, increasing the difficulty of subsequent sorting and purification. The lower the spatial distribution complexity, the higher the resource utilization rate; conversely, more crushing and sorting costs are required. Therefore, spatial distribution complexity characterizes the occurrence state of minerals in gangue, while the degree of liberation of vanadium-titanium magnetite characterizes the separation potential of minerals under this occurrence state. Generally, the more complex the spatial distribution, the more uneven the embedding, and the more obvious the intergrowth and encapsulation, the more difficult it is to liberate individual particles, and the lower the degree of liberation. Conversely, if the spatial distribution is relatively uniform, the mineral boundaries are relatively clear, and the aggregation and encapsulation phenomena are weak, it is easier to form liberated individual particles, and the degree of liberation is relatively high. By revealing the relationship between the internal structural state of the ore and the ease of subsequent mining, crushing, and grinding, both provide a clear correlation logic for the construction of subsequent mapping relationships and are the key link connecting mineralogical characteristics and mineability assessment. In this embodiment of the invention, the mineralogical analysis module 120 is used to perform mineralogical analysis on vanadium-titanium magnetite core samples to determine the spatial distribution complexity of vanadium-titanium magnetite in gangue and the degree of liberation of vanadium-titanium magnetite. The degree of liberation of vanadium-titanium magnetite is the ratio of the number of liberated individual vanadium-titanium magnetite particles to the total number of mineral particles. Determining the spatial distribution complexity of vanadium-titanium magnetite in gangue includes: Vanadium-titanium magnetite core samples underwent directional cutting, resin embedding, stepwise grinding, and mirror polishing to prepare standard cross-section samples that meet the requirements of micromineralogical analysis. Specifically, high-precision directional cutting equipment (cutting accuracy controlled within ±0.1 mm) was used to directionally cut the vanadium-titanium magnetite core samples, with the cutting surface perpendicular to the core axis, resulting in core slices with a thickness of 5-8 mm. The core slices were placed in a special embedding mold, and epoxy resin embedding agent (epoxy resin to curing agent ratio of 4:1) was poured in, ensuring that the core slices were completely coated with the embedding agent. The molds were then placed in a constant temperature drying oven and cured at 60℃ for 24 hours before embedding. After the agent has completely solidified, it is removed to obtain the mounted sample. The mounted sample is processed using a step-by-step grinding method. First, coarse grinding is performed using 200-grit diamond sandpaper to remove residual mounting agent and cutting marks from the sample surface. Then, fine grinding is performed sequentially using 400-grit, 800-grit, 1200-grit, and 2000-grit diamond sandpaper. After each level of grinding, the sample surface is rinsed with deionized water to ensure that no grinding debris remains. A polishing machine (using velvet material for the polishing cloth and diamond polishing paste with a particle size of 1μm) is used for mirror polishing until the surface of the mounted sample is free of scratches and dents and has a uniform luster, thus obtaining a standard cross-section sample that meets the imaging requirements for micromineralogical analysis. A mineral parameter automatic analysis system was used to perform scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS) elemental analysis on standard cross-sectional samples. This generated mineral spatial distribution data including mineral type, particle centroid coordinates, particle boundary contours, and particle area. Specifically, the standard cross-sectional sample was fixed on the sample stage of the mineral parameter automatic analysis system (MLA). The sample position was adjusted to ensure the sample surface was perpendicular to the imaging lens. The SEM parameters were set as follows: accelerating voltage 15kV, magnification 500-1000x, scanning step size 0.5μm, and scanning range covering the entire standard cross-sectional sample. The SEM was then activated for imaging, and the EDS elemental analysis function was simultaneously enabled to perform a full-section elemental scan of the sample. The EDS resolution was set to 0.1wt%, and the types and contents of each element in the sample were collected. The system automatically identified the mineral type and recorded the centroid coordinates (accurate to 0.1μm), particle boundary contours (precisely described using pixel coordinates), and particle area (in μm²) of each mineral particle, generating mineral spatial distribution data including mineral type, particle centroid coordinates, particle boundary contours, and particle area. The standard cross-sectional sample is divided into different spatial statistical units according to a preset grid size. The volume fraction of vanadium-titanium magnetite in each spatial statistical unit is calculated based on the mineral spatial distribution data. Specifically, according to the preset grid size (1mm×1mm), the standard cross-sectional sample is divided into spatial statistical units using the grid division function of the automatic mineral parameter analysis system. The spatial statistical units are numbered and their coordinate positions are recorded. For each spatial statistical unit, the sum of the areas of all vanadium-titanium magnetite particles in each spatial statistical unit is calculated based on the mineral spatial distribution data. Combined with the sample thickness, the volume of vanadium-titanium magnetite in each spatial statistical unit is calculated (the volume is the product of the sum of the particle areas and the sample thickness). Then, the ratio of the volume of vanadium-titanium magnetite in each spatial statistical unit to the total volume of the unit (the total volume of the unit is the product of the unit area and the sample thickness) is calculated to obtain the volume fraction of vanadium-titanium magnetite in each spatial statistical unit. The volume fraction of vanadium-titanium magnetite in all spatial statistical units was statistically analyzed, and the spatial coefficient of variation was calculated. This spatial coefficient of variation was used as the spatial distribution complexity of vanadium-titanium magnetite to characterize the non-uniformity of its distribution in gangue. Specifically, the volume fraction of vanadium-titanium magnetite in all spatial statistical units was statistically analyzed to form a spatial statistical sequence of standard cross-section samples. The mean volume fraction and standard deviation of the spatial statistical sequence were calculated. The mean volume fraction characterizes the overall vanadium-titanium magnetite occurrence level of the sample, and the standard deviation characterizes the degree of volume fraction fluctuation between different spatial statistical units. The ratio of the standard deviation to the mean volume fraction was used as the spatial coefficient of variation to eliminate the influence of absolute content differences on the evaluation of distribution fluctuation. A larger spatial coefficient of variation indicates a more significant difference in the volume fraction of vanadium-titanium magnetite between different spatial statistical units, a more non-uniform mineral distribution, and higher spatial distribution complexity. Conversely, a smaller spatial coefficient of variation indicates a more uniform distribution of vanadium-titanium magnetite in gangue and lower spatial distribution complexity.

[0022] The tensor decomposition module decomposes the third-order magnetic gradient tensor data to obtain tensor decomposition parameters, including the tensor decomposition rank, weight dispersion coefficients, and direction dispersion coefficients. The tensor decomposition rank characterizes the number of core dimensions in the third-order magnetic gradient tensor data, reflecting the aggregation hierarchy and structural dimensions of magnetic materials within vanadium-titanium magnetite. A larger rank indicates higher complexity of the magnetic gradient tensor data, corresponding to a more complex internal structure and more layers of magnetic material distribution within the vanadium-titanium magnetite. The tensor decomposition rank provides dimensional support for subsequent structural complexity calculations. The weight dispersion coefficients characterize the dispersion of the weight values ​​of each component after the third-order magnetic gradient tensor decomposition, reflecting the uniformity of magnetic material distribution within the vanadium-titanium magnetite. A larger weight dispersion coefficient indicates greater dispersion of the weight values ​​of each component. The greater the weight difference, the more uneven the distribution of magnetic materials inside the mineral. The weight dispersion coefficient quantifies the distribution characteristics of magnetic materials, helps to judge the uniformity of the internal structure of the mineral, and improves the comprehensiveness of the structural complexity calculation. The directional dispersion coefficient is used to characterize the dispersion of the directional vectors of each component after the decomposition of the third-order magnetic gradient tensor. It reflects the consistency of the arrangement direction of magnetic particles inside vanadium-titanium magnetite. The larger the directional dispersion coefficient, the more disordered the arrangement direction of magnetic particles, and the more irregular the internal structure of the mineral. Its function is to quantify the arrangement characteristics of magnetic particles, supplement the directional information of the internal structure of the mineral, and ensure that the structural complexity calculation can fully cover the core features of the dimensions, distribution and direction inside the mineral, and provide data support for subsequent structural complexity calculation and exploitability assessment. In this embodiment of the invention, the tensor decomposition module 130 is used to decompose the third-order magnetic gradient tensor data, determine the tensor decomposition rank, weight distribution characteristics, and direction distribution characteristics corresponding to the third-order magnetic gradient tensor, and calculate the structural complexity inside the vanadium-titanium magnetite at each sounding location, including: By decomposing the third-order magnetic gradient tensor data, tensor decomposition parameters at each sounding location are obtained. These parameters include the tensor decomposition rank, weight dispersion coefficients, and direction dispersion coefficients. The decomposition process can be either CP decomposition or Tucker decomposition. Specifically, taking Tucker decomposition as an example, the core tensor dimension is set to 3×3×3, the decomposition rank range is 3-8, the number of iterations is 1000, and the convergence threshold is 1e-6. Decomposition is performed using gradient descent to obtain the core tensor and the factor matrices of each mode. Based on the decomposition results, tensor decomposition parameters at each sounding location are extracted. The tensor decomposition rank is the optimal rank determined during the decomposition process (determined through cross-validation, selecting the rank with the smallest fitting error as the optimal value). The weight dispersion coefficient is the ratio of the standard deviation to the mean of each component weight value, and the direction dispersion coefficient is the standard deviation of the angle between the direction vectors of each component. The tensor decomposition parameters of all sounding locations are organized in sounding order to form a tensor decomposition parameter dataset, with the sounding location corresponding to each parameter labeled for subsequent standardization contribution calculation. Based on the distribution characteristics of the tensor decomposition parameters, the standardized contribution of each tensor decomposition parameter is determined, and the standardized contribution is used as a weight to perform a weighted summation on each tensor decomposition parameter to obtain the structural complexity of the vanadium-titanium magnetite at the corresponding sounding location. The specific steps for determining the standardized contribution of each tensor decomposition parameter based on its distribution characteristics include: The tensor decomposition parameters at all depth sounding locations in the target mining area are statistically analyzed. Specifically, the tensor decomposition rank, weighted discrete coefficient, and directional discrete coefficient of all depth sounding locations are extracted from the tensor decomposition parameter dataset and constructed as independent parameter sequences. The standard deviations of each tensor decomposition parameter within the target mining area are calculated to characterize the sensitivity of the corresponding tensor decomposition parameter to the spatial differences of the ore body. Specifically, the standard deviations of the tensor decomposition rank, weighted dispersion coefficients, and directional dispersion coefficients are calculated based on the parameter sequence. These standard deviations directly characterize the sensitivity of the corresponding parameter to the spatial differences of the ore body. The larger the standard deviation, the more obvious the parameter changes with depth and the more sensitive it is to the spatial differences of the ore body. The ratio of the standard deviation of each tensor decomposition parameter to the sum of the standard deviations of all tensor decomposition parameters is taken as the standardization contribution of the corresponding tensor decomposition parameter.

[0023] The mapping relationship construction module is used to establish a quantitative correlation between mineralogical characteristic parameters (spatial distribution complexity, vanadium-titanium magnetite liberation degree) and magnetically derived parameters (structural complexity), building a key bridge from magnetic measurement data to mineability assessment, and realizing accurate conversion and mutual verification among the three. It establishes a calculable, transferable, and predictable correlation bridge between core mineralogical analysis results and third-order magnetic gradient tensor decomposition results, forming a unified data mapping chain between measured mineralogical properties at finite sounding locations and magnetic response structural characteristics obtainable across the entire sounding range. This significantly improves the extrapolation capability of finite core samples to all sounding locations in the entire mining area, reduces reliance on intensive coring and large-scale mineralogical tests, improves the efficiency and accuracy of continuous evaluation of deep vanadium-titanium magnetite, and provides intermediate predictive parameters with mineralogical interpretation basis for subsequent mineability assessment, enhancing the reliability and engineering applicability of the evaluation results. The first and second mapping relationships have different physical meanings and functions. The first mapping relationship characterizes how the spatial distribution of vanadium-titanium magnetite in gangue affects the degree of liberation of individual mineral particles. Specifically, a more uniform spatial distribution, clearer boundaries, and weaker inclusions and intergrowths generally favor the formation of liberated individual particles, resulting in a relatively higher degree of liberation. Conversely, a more complex spatial distribution, greater local enrichment differences, and more pronounced inclusions and intergrowths typically lead to a lower degree of liberation. Therefore, the first mapping relationship essentially reflects the mineralogical law of occurrence state versus separation result. The second mapping relationship characterizes the third-order magnetic gradient tensor... The structural complexity obtained from the solution corresponds to the spatial distribution complexity of minerals in gangue. That is, the more numerous, unbalanced, and dispersed the magnetic response modes are, the more complex the internal occurrence of the ore body and the more uneven the spatial distribution. Therefore, the second mapping relationship essentially reflects the geophysical and mineralogical correspondence between magnetic response structural characteristics and mineral spatial distribution. The two together form a two-level mapping path from magnetic response to dissociation capability, so that even if the depth sounding position of the core sample cannot be directly obtained, the spatial distribution complexity can be predicted first from the structural complexity, and then the degree of dissociation can be further predicted from the spatial distribution complexity. In this embodiment of the invention, the mapping relationship construction module 140 is used to construct a first mapping relationship between spatial distribution complexity and the degree of liberation of vanadium-titanium magnetite, and a second mapping relationship between structural complexity and spatial distribution complexity. This includes: using the sounding location with vanadium-titanium magnetite core samples as the calibration sounding location; extracting the spatial distribution complexity, degree of liberation, and structural complexity at the calibration sounding location to construct a calibration sample dataset; based on the calibration sample dataset, fitting the relationship between spatial distribution complexity and degree of liberation to establish a first mapping relationship between spatial distribution complexity and the degree of liberation of vanadium-titanium magnetite, used to characterize the influence of changes in spatial distribution complexity on changes in degree of liberation; based on the calibration sample dataset, fitting the relationship between structural complexity and spatial distribution complexity to establish a second mapping relationship between structural complexity and spatial distribution complexity, used to characterize the correspondence between magnetic response structural characteristics and the spatial distribution state of the mineral. Specifically, vanadium-titanium magnetite core samples already obtained within the target mining area are selected. All depth sounding locations are identified as calibration depth sounding locations, ensuring that these locations are distributed across different areas and depth ranges within the target mining area, covering different distribution states and structural characteristics of vanadium-titanium magnetite. The spatial distribution complexity and vanadium-titanium magnetite liberation degree corresponding to all calibration depth sounding locations are extracted from the mineralogical analysis module, and the structural complexity is extracted from the tensor decomposition module. The consistency of the three sets of parameters is verified to ensure that each calibration depth sounding location corresponds to a complete set of spatial distribution complexity-liberation degree-structural complexity parameters. All calibration depth sounding locations and their corresponding parameters are organized in depth sounding order to construct a calibration sample dataset. This dataset can be presented in tabular form, containing four columns: depth sounding location, spatial distribution complexity, vanadium-titanium magnetite liberation degree, and structural complexity. The fitting process for the first and second mapping relationships is the same. Taking the fitting process for the first mapping relationship as an example, it includes: based on the constructed calibration sample dataset, extracting the spatial distribution complexity of all calibration depth sounding locations (denoted as...). ) and the corresponding degree of dissociation (denoted as ) ),Will As an independent variable, As the dependent variable, import it into professional data fitting software (such as MATLAB, Origin, SPSS); prioritize linear fitting and quadratic polynomial fitting, with the linear fitting model being... ( , (where are the fitting coefficients), the quadratic polynomial fitting model is: ( , , (These are the fitting coefficients); the fitting coefficients are solved using the least squares method, and the goodness of fit is calculated to ensure that the goodness of fit is ≥0.85. If the goodness of fit does not meet the standard, the fitting model is adjusted (e.g., replaced with cubic polynomial fitting) and the solution is recalculated. After the fitting is completed, the effectiveness of the fitting model is verified. Ten calibration depth measurement position parameters that were not involved in the fitting are substituted into the fitting model, and the predicted value of the liberation degree of vanadium-titanium magnetite is calculated. The error between the predicted value and the measured value is controlled within ±5%. After the verification is passed, the fitting model is determined as the first mapping relationship, and the specific values ​​of each fitting coefficient in the fitting model are determined (retaining four decimal places).

[0024] In this embodiment of the invention, the mineability assessment module 150 is used to assess the mineability of vanadium-titanium magnetite at different depth locations based on the structural complexity of the vanadium-titanium magnetite at each sounding location, combined with a first mapping relationship and a second mapping relationship, including: The structural complexity of the vanadium-titanium magnetite at each sounding location is obtained, and the structural complexity is input into the second mapping relationship to obtain the predicted value of the spatial distribution complexity at the corresponding sounding location. Input the spatial distribution complexity prediction value into the first mapping relationship, and calculate the vanadium-titanium magnetite liberation degree prediction value at the corresponding sounding location; The exploitability evaluation index for each sounding location is obtained by weighted summing of the reciprocals of the structural complexity parameter, the reciprocal of the predicted spatial distribution complexity, and the predicted liberation degree of vanadium-titanium magnetite at each sounding location. The weighting process can be as follows: the reciprocals of the structural complexity parameter, the reciprocal of the predicted spatial distribution complexity, and the predicted liberation degree of vanadium-titanium magnetite at each sounding location in the calibration sample dataset are used as the first, second, and third evaluation indicators, respectively, and the beneficiation recovery rate corresponding to each calibration sample is obtained simultaneously as the development efficiency indicator. The absolute values ​​of the Pearson correlation coefficients between the three evaluation indicators and the development efficiency indicator are calculated respectively, and the sum of the absolute values ​​of the Pearson correlation coefficients of the three is used as the normalization benchmark. The weight values ​​are obtained by the ratio of the absolute values ​​of the Pearson correlation coefficients corresponding to the first, second, and third evaluation indicators to the normalization benchmark. Locations with a exploitability evaluation index greater than a preset exploitability evaluation threshold are designated as priority mining areas, while locations with an exploitability evaluation index less than or equal to the preset exploitability evaluation threshold are designated as temporarily deferred mining areas. The preset exploitability evaluation threshold can be set by quantiles based on the statistical distribution of the exploitability evaluation index of all locations, with the 75th percentile value being used as the preset exploitability evaluation threshold.

[0025] Please see Figure 2 , Figure 2 This is a flowchart illustrating a method for multidimensional spatial analysis of vanadium-titanium magnetite based on third-order tensor decomposition provided in an embodiment of the present invention, including: Acquire vanadium-titanium magnetite core samples from the target mining area and the third-order magnetic gradient tensor data at the corresponding depth sounding locations; Mineralogical analysis was performed on vanadium-titanium magnetite core samples to determine the spatial distribution complexity of vanadium-titanium magnetite in gangue and the degree of vanadium-titanium magnetite liberation. The degree of vanadium-titanium magnetite liberation is the ratio of the number of liberated individual vanadium-titanium magnetite particles to the total number of mineral particles. The third-order magnetic gradient tensor data is decomposed to determine the tensor decomposition rank, weight distribution characteristics and directional distribution characteristics of the third-order magnetic gradient tensor, and the structural complexity of the vanadium-titanium magnetite at each sounding location is calculated. We construct a first mapping relationship between spatial distribution complexity and the dissociation degree of vanadium-titanium magnetite, and a second mapping relationship between structural complexity and spatial distribution complexity. Based on the structural complexity of the vanadium-titanium magnetite at each sounding location, combined with the first and second mapping relationships, the mineability of the vanadium-titanium magnetite at different sounding locations is assessed.

[0026] Please refer to Figure 3 The present invention also provides an electronic device 300, including a memory 310, a processor 320, and a communication bus 330; the memory 310 and the processor 320 are connected via the communication bus 330. The memory 310 stores a method for multidimensional spatial analysis of vanadium-titanium magnetite based on third-order tensor decomposition, which can be loaded and executed by the processor 320 as provided in the above embodiments.

[0027] The memory 310 can be used to store instructions, programs, code, code sets, or instruction sets. The memory 310 may include a program storage area and a data storage area. The program storage area may store instructions for implementing an operating system, instructions for at least one function, and instructions for implementing the vanadium-titanium magnetite multidimensional spatial analysis method based on third-order tensor decomposition provided in the above embodiments. The data storage area may store data involved in the vanadium-titanium magnetite multidimensional spatial analysis method based on third-order tensor decomposition provided in the above embodiments.

[0028] Processor 320 may include one or more processing cores. Processor 320 executes instructions, programs, code sets, or instruction sets stored in memory 310, and calls data stored in memory 310 to perform various functions and process data according to the present invention. Processor 320 may be at least one of the following: Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Digital Signal Processing Device (DSPD), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), Central Processing Unit (CPU), Controller, Microcontroller, and Microprocessor. It is understood that, for different devices, the electronic devices used to implement the functions of processor 320 may be other types, and the embodiments of the present invention do not specifically limit this.

[0029] The communication bus 330 may include a path for transmitting information between the aforementioned components. The communication bus 330 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. The communication bus 330 can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 3 The symbol is represented by a single double arrow, but this does not mean that there is only one bus or one type of bus.

[0030] This invention provides a computer-readable storage medium storing a computer program that can be loaded by a processor and executed as described in the above embodiments, a method for multidimensional spatial analysis of vanadium-titanium magnetite based on third-order tensor decomposition.

[0031] In this embodiment of the invention, the computer-readable storage medium can be a tangible device that holds and stores instructions used by an instruction execution device. The computer-readable storage medium can be, but is not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof. Specifically, the computer-readable storage medium can be a portable computer disk, a hard disk, a USB flash drive, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), lectern random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory stick, floppy disk, optical disk, magnetic disk, mechanical encoding device, or any combination thereof.

[0032] The terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0033] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of this application is not limited to the technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the foregoing concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions claimed in this invention.

Claims

1. A multidimensional spatial analysis system for vanadium-titanium magnetite based on third-order tensor decomposition, characterized in that, include: The data acquisition module is used to acquire vanadium-titanium magnetite core samples from the target mining area and the third-order magnetic gradient tensor data at the corresponding depth sounding locations. The mineralogical analysis module is used to perform mineralogical analysis on vanadium-titanium magnetite core samples to determine the spatial distribution complexity of vanadium-titanium magnetite in gangue and the degree of liberation of vanadium-titanium magnetite. The degree of liberation of vanadium-titanium magnetite is the ratio of the number of liberated individual vanadium-titanium magnetite particles to the total number of mineral particles. The tensor decomposition module is used to decompose the third-order magnetic gradient tensor data, determine the tensor decomposition rank, weight distribution characteristics and directional distribution characteristics of the third-order magnetic gradient tensor, and calculate the structural complexity of the vanadium-titanium magnetite at each sounding location. The mapping relationship construction module is used to construct the first mapping relationship between spatial distribution complexity and the dissociation degree of vanadium-titanium magnetite, and the second mapping relationship between structural complexity and spatial distribution complexity. The mineability assessment module is used to assess the mineability of vanadium-titanium magnetite at different depth locations based on the internal structural complexity of the vanadium-titanium magnetite, combined with a first mapping relationship and a second mapping relationship.

2. The vanadium-titanium magnetite multidimensional spatial analysis system based on third-order tensor decomposition according to claim 1, characterized in that, The specific execution steps of the data acquisition module for acquiring third-order magnetic gradient tensor data include: acquiring time-domain measurement signals of the magnetic field at each depth measurement location in the well using a rotating magnetic sensor; performing a Fourier transform on the time-domain measurement signals of the magnetic field to obtain frequency-domain spectral data at the corresponding depth measurement location, thus completing the conversion from time-domain signal to frequency-domain signal; extracting the corresponding magnetic gradient tensor components according to different frequency orders based on the frequency-domain spectral data, and recombining the components according to the arrangement rules of the third-order spatial derivative tensor to generate third-order magnetic gradient tensor data at each depth location.

3. The vanadium-titanium magnetite multidimensional spatial analysis system based on third-order tensor decomposition according to claim 1, characterized in that, The specific steps for determining the spatial distribution complexity of vanadium-titanium magnetite in gangue in the mineralogical analysis module include: Vanadium-titanium magnetite core samples were directionally cut, resin-mounted, progressively ground, and mirror-polished to prepare standard cross-section samples that meet the requirements of micromineralogical analysis. An automatic mineral parameter analysis system was used to perform scanning electron microscopy and energy dispersive spectroscopy on standard cross-section samples to generate mineral spatial distribution data including mineral type, particle centroid coordinates, particle boundary contours, and particle area. The standard cross-section sample is divided into different spatial statistical units according to the preset grid size, and the volume fraction of vanadium-titanium magnetite in each spatial statistical unit is calculated based on the mineral spatial distribution data. The volume fraction of vanadium-titanium magnetite in all spatial statistical units is statistically analyzed and the spatial variation coefficient is calculated. The spatial variation coefficient is used as the spatial distribution complexity of vanadium-titanium magnetite to characterize the non-uniform distribution of vanadium-titanium magnetite in gangue.

4. The vanadium-titanium magnetite multidimensional spatial analysis system based on third-order tensor decomposition according to claim 1, characterized in that, The specific execution steps for calculating the internal structural complexity of vanadium-titanium magnetite at each depth sounding location in the tensor decomposition module include: By decomposing the third-order magnetic gradient tensor data, tensor decomposition parameters at each sounding location are obtained. The tensor decomposition parameters include tensor decomposition rank, weighted discrete coefficients, and directional discrete coefficients. The decomposition process can be either CP decomposition or Tucker decomposition. Based on the distribution characteristics of the tensor decomposition parameters, the standardized contribution of each tensor decomposition parameter is determined, and the standardized contribution is used as a weight to perform a weighted summation of each tensor decomposition parameter to obtain the structural complexity of the vanadium-titanium magnetite at the corresponding sounding location.

5. The vanadium-titanium magnetite multidimensional spatial analysis system based on third-order tensor decomposition according to claim 4, characterized in that, The specific execution steps for determining the standardized contribution of each tensor decomposition parameter based on the distribution characteristics of the tensor decomposition parameters include: Statistical analysis of tensor decomposition parameters at all depth sounding locations in the target mining area; The standard deviations of each tensor decomposition parameter within the target mining area are calculated to characterize the sensitivity of the corresponding tensor decomposition parameters to the spatial differences of the ore body. The ratio of the standard deviation of each tensor decomposition parameter to the sum of the standard deviations of all tensor decomposition parameters is taken as the standardization contribution of the corresponding tensor decomposition parameter.

6. The vanadium-titanium magnetite multidimensional spatial analysis system based on third-order tensor decomposition according to claim 1, characterized in that, The specific execution steps of the mapping relationship construction module include: using the sounding location with vanadium-titanium magnetite core samples as the calibration sounding location, extracting the spatial distribution complexity, dissociation degree, and structural complexity at the calibration sounding location, and constructing a calibration sample dataset; based on the calibration sample dataset, fitting the relationship between spatial distribution complexity and dissociation degree to establish a first mapping relationship between spatial distribution complexity and the dissociation degree of vanadium-titanium magnetite, used to characterize the influence of changes in spatial distribution complexity on changes in dissociation degree; based on the calibration sample dataset, fitting the relationship between structural complexity and spatial distribution complexity to establish a second mapping relationship between structural complexity and spatial distribution complexity, used to characterize the correspondence between magnetic response structural characteristics and mineral spatial distribution state.

7. The vanadium-titanium magnetite multidimensional spatial analysis system based on third-order tensor decomposition according to claim 1, characterized in that, The specific executable steps of the exploitability assessment module include: The structural complexity of the vanadium-titanium magnetite at each sounding location is obtained, and the structural complexity is input into the second mapping relationship to obtain the predicted value of the spatial distribution complexity at the corresponding sounding location. Input the spatial distribution complexity prediction value into the first mapping relationship, and calculate the vanadium-titanium magnetite liberation degree prediction value at the corresponding sounding location; The exploitability evaluation index at each sounding location is obtained by weighted summing of the reciprocal of the structural complexity parameter, the reciprocal of the predicted spatial distribution complexity, and the predicted degree of liberation of vanadium-titanium magnetite at each sounding location. Locations with a exploitability evaluation index greater than the preset exploitability evaluation threshold are designated as priority mining areas, while locations with an exploitability evaluation index less than or equal to the preset exploitability evaluation threshold are designated as temporarily deferred mining areas.

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