A method for optimizing the inverted floating cone boundary based on polar coordinate discretization

Abstract

The application discloses a polar coordinate discretization-based inverted floating cone boundary optimization method and belongs to the technical field of open-pit mining. The method is characterized in that: the inverted floating cone model is constructed by means of angle difference in polar coordinates, the inverted floating model is subjected to discretization index processing, and the boundary optimization is carried out by using a block model; the slope angle interpolation processing based on polar coordinates is adopted, the step of setting the chamfer in a large amount of manual interaction mode required by traditional slope design is effectively avoided, and the slope can be automatically designed according to the principle of conservative value; the inverted floating cone moving speed is accelerated by using the sequence index-based mode, the index value is adopted according to the translation invariance characteristics of the inverted floating cone, and the calculation speed is effectively improved. Compared with the traditional inverted floating cone method, the application can not only calculate more reasonable economic value, but also significantly reduce the calculation complexity and greatly shorten the time for generating the final boundary with the optimal economic value. Meanwhile, when the coal price fluctuates, the final boundary can be quickly adjusted by using the method, so that the flexibility and economic benefits of the mining decision are improved.

Description

Technical Field

[0001] This invention belongs to the field of open-pit mining technology, and specifically relates to an optimization method for the boundary of an inverted floating cone based on polar coordinate discretization. Background Technology

[0002] In open-pit mining, common boundary optimization methods include the floating cone method, the inverted floating cone elimination method, graph theory, linear programming, and dynamic programming. However, some methods fail to maximize economic value in the final boundary they generate; while others, although capable of optimizing economic value, are less effective in situations involving massive amounts of data and complex coal seam geological information. Therefore, the traditional inverted floating cone elimination method, as an intuitive and physically clear approach, has been widely tried in the industry. This method approximates the optimal boundary by eliminating uneconomical cone regions. However, it has obvious limitations in engineering practice: First, traditional methods usually construct cones based on a single or average slope angle, which cannot accurately reflect the real geological conditions and slope angle requirements of the mining area with anisotropy, resulting in deviations in the optimization results in terms of safety or economy; Second, its core calculation process involves a large number of geometric inclusion relationship judgments on the three-dimensional block model, and the computational complexity increases exponentially with the improvement of model accuracy. When faced with massive block data, the generation of the final boundary takes too long and is heavily dependent on computing hardware; Finally, when market prices and cost parameters change, the entire optimization process often needs to be recalculated from scratch, making it difficult to achieve rapid dynamic evaluation and adjustment of mining schemes and lacking the flexibility to cope with market fluctuations. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the purpose of this invention is to provide an optimization method for the boundary of an inverted floating cone based on polar coordinate discretization.

[0004] The technical solution adopted in this invention is: an optimization method for the boundary of an inverted floating cone based on polar coordinate discretization, the key technical points of which include the following steps:

[0005] S1, Initial boundary for generating block values: Based on the preset coal price and block burial depth, the coal-rock ratio in the initial boundary model is converted into economic value, and an initial block model based on economic value is established.

[0006] S2, Fitting the slope angle difference curve: In the polar coordinate system, according to the slope angle parameters corresponding to different directions in the mining area, the interpolation function is used to fit the discrete direction angle-slope angle point set to generate a continuous direction angle-slope angle difference curve.

[0007] S3. Based on the difference curve and the maximum mining depth, determine the overall geometric shape of the block; combine the difference curve and the layer height parameter to generate closed curves that divide the inside and outside of the block in each layer; by traversing layer by layer along the mining depth direction, obtain the effective blocks on each plane, and convert the absolute index of the effective blocks into a relative index relative to the central block to construct a discrete inverted cone model based on polar coordinates.

[0008] S4. The discrete inverted cone model is used to remove the inverted cone from the initial block boundary to obtain the final mining boundary that satisfies the multi-directional slope angle constraints and optimizes economic value.

[0009] In the above scheme, the process of establishing an initial block model based on economic value in step S1 specifically includes:

[0010] S11, provides Q, which includes the quantity of block coal. i Block stripping ratio λ i and the burial depth d of the block i The initial level model of information;

[0011] S12, based on the preset coal price P c Unit stripping cost C s and depth-related cost function f(d) i ), calculate the economic value Vi of each block, using the following formula:

[0012] V i =Q i ·P c -[Q i ·(1+λ i )]·C s -f(d i )

[0013] In the formula, Q i ·P c This represents the revenue from bulk coal resources; (Q) i ·λ i )·C s f(d) represents the stripping cost corresponding to the amount of coal; i ) represents the additional cost or reduction function related to depth;

[0014] S13, assign a corresponding economic value V to each block in the initial boundary model. i Thus, the initial block model based on economic value is established.

[0015] In the above scheme, step S2, which involves fitting the discrete direction angle-slope angle point set using an interpolation function, specifically includes:

[0016] S21, Obtain a discrete set of points consisting of multiple orientation angle-slope angle data pairs, where each data pair includes an orientation angle and its corresponding design slope angle;

[0017] S22, assign the derivative value to zero for each data point in the discrete point set to meet the conservative value selection principle of slope design; S23, use the discrete point set and the derivative value corresponding to each data point as input, and construct a piecewise polynomial function as the difference curve using the Hermite interpolation method; wherein, for each data point in the discrete point set, the function value of the difference curve at that point is equal to the given design slope angle, and the derivative value at that point is equal to the given zero value; S24, output the difference curve to determine the slope angle under any direction angle.

[0018] In the above scheme, determining the geometric shape of the overall block in step S3 includes the following steps:

[0019] Define an inverted conical geometric boundary in three-dimensional space, constrained by the difference curve and the maximum mining depth.

[0020] The geometric boundary is constructed in the following layered manner: the maximum mining depth range is divided into multiple horizontal layers according to a preset layer height. For each depth layer, a contour radius that varies with the direction angle on the horizontal plane is calculated based on the depth value of the layer and the difference curve.

[0021] The geometric shape of the overall block is the closed volume defined in three-dimensional space by the contour radii corresponding to all depth layers and varying with the direction angle.

[0022] In the above scheme, the method for obtaining the effective blocks on each plane in step S3 is as follows: for any block to be judged located in the layer, its horizontal position is converted to polar coordinates with the center of the cone as the pole to obtain its polar radius and direction angle; if the polar radius of the block is not greater than the contour radius corresponding to the direction angle, then the block is determined to be within the boundary of the geometric shape.

[0023] In the above scheme, the construction of the discrete inverted floating cone model based on polar coordinates in step S3 means converting the absolute spatial index of all the blocks that are determined to be valid into a relative index offset relative to the predefined center block index of the inverted floating cone.

[0024] The set of relative index offsets constitutes the discrete inverted floating cone model, which is used for mask matching and neighborhood calculation in the subsequent inverted floating cone elimination process.

[0025] In the above scheme, step 4, generating the final optimized state, refers to:

[0026] Calculate the total economic value of all blocks in the set of valid blocks;

[0027] Determine whether the total economic value is less than or equal to zero;

[0028] If the total economic value is less than or equal to zero, the set of valid blocks is excluded from the initial block boundary to update the boundary.

[0029] The beneficial effects of this invention are as follows: A method for optimizing the boundary of an inverted floating cone based on polar coordinate discretization is proposed. This method innovatively constructs an inverted floating cone model in polar coordinates through angle differences, performs discretization and indexing processing on the inverted floating model, and uses a block model for boundary optimization. It employs slope angle interpolation based on polar coordinates, effectively avoiding the steps of setting chamfers manually in traditional slope design, and can automatically design slopes based on the principle of conservative value selection. It accelerates the movement speed of the inverted floating cone using a sequence indexing method. Based on the translation invariance of the inverted floating cone calculation, indexing is used to effectively improve the calculation speed. Compared with traditional inverted floating cone methods, this invention not only calculates a more reasonable economic value but also significantly reduces computational complexity and greatly shortens the time for generating the final boundary with the optimal economic value. Furthermore, when coal prices fluctuate, this method can quickly adjust the final boundary, thereby improving the flexibility and economic efficiency of mining decisions. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a flowchart of the inverted floating cone boundary optimization method based on polar coordinate discretization according to the present invention;

[0032] Figure 2 This is a schematic diagram of the direction angle-slope angle interpolation curve of the present invention;

[0033] Figure 3 This is the initial boundary diagram in an embodiment of the present invention;

[0034] Figure 4 This is a schematic diagram of the block division result forming a layer in an embodiment of the present invention;

[0035] Figure 5 This is a schematic diagram of a discretized inverted floating cone model in an embodiment of the present invention;

[0036] Figure 6This is a schematic diagram of the final optimized state in an embodiment of the present invention. Detailed Implementation

[0037] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the following description is provided in conjunction with the accompanying drawings. Figures 1-6 The present invention will be further described in detail below with reference to specific embodiments.

[0038] The embodiment of this invention employs an inverted floating cone boundary optimization method based on polar coordinate discretization, such as... Figure 1 As shown, it includes the following steps:

[0039] Step 1: The initial stage of generating block assignments.

[0040] This method first converts the coal-rock ratio in the initial boundary model into corresponding economic value based on the preset coal price and block burial depth, thereby establishing an initial block model based on economic value.

[0041] Based on the preset coal price P c and the burial depth d of the block i This transforms the coal-rock ratio in the initial boundary model into economic value. Let Q be the amount of coal in the i-th block. i The stripping ratio is λ i The unit divestiture cost is c s Then the economic value of the block V i The calculation formula is:

[0042] V i =Q i ·P c -[Q i ·(1+λ i )]·C s -f(d i )

[0043] in:

[0044] Q i ·P c This indicates the revenue from bulk coal resources;

[0045] (Q i ·λ i )·C s This represents the stripping cost corresponding to the amount of coal;

[0046] f(d i ) represents the additional costs or reduction functions that are deeply related (e.g., road construction, drainage, and transportation costs), which can be modeled as f(d i )=αd i (where α is the depth cost coefficient).

[0047] Step 2: Fit the difference curve, such as Figure 2 As shown.

[0048] Due to significant differences in geological conditions across the mine, the slope angles vary in different directions. In the traditional inverted cone elimination method, the cone angle directly affects the slope angle constraint. Therefore, this embodiment introduces the slope angle parameters for each direction into a polar coordinate system. Let the direction angle be θ, and its corresponding slope angle be β, then it can be expressed as:

[0049]

[0050] Where, θ i Let β represent the i-th direction angle. i This represents the actual slope angle in that direction.

[0051] To obtain the slope angle value under arbitrary direction angles, this embodiment uses the Hermite interpolation function for the discrete point set. Fitting is performed. Hermite interpolation requires not only that the interpolating polynomial and the interpolated function have the same function values ​​at the nodes, but also that their derivatives are equal, ensuring the smoothness of the slope angle. Its interpolation function can be expressed as:

[0052]

[0053] Meanwhile, in accordance with the principle of conservative values ​​in slope design, the derivative of each discrete point is specified to be 0 and at its maximum value to ensure that other areas have gentler slopes and guarantee safety.

[0054] Step 3: Generate a discrete inverted floating cone model.

[0055] Based on the difference curve and the maximum mining depth, the overall geometric shape of the block can be determined. Subsequently, combining the difference curve and layer height parameters, closed curves are generated within each layer to divide the block inside and outside: blocks inside the closed curve are considered valid blocks, while those outside the curve are considered invalid blocks. By traversing layer by layer along the z-axis, the valid blocks on each XY plane can be obtained, and a discrete inverted cone model based on the polar coordinate difference curve can be constructed.

[0056] Since the coordinates of each point within the cone do not depend on its absolute position during the cone's movement, but only on its internal relative relationship, the absolute index of the effective blocks in the model can be converted into a relative index relative to the central block to generate a discrete inverted cone model, thereby improving the computational efficiency of the subsequent inverted cone elimination process.

[0057] (1) Layer depth

[0058] z k = kh, k = 0, 1, K

[0059] The layer height is h, and the layer number is k. Dmax is the maximum depth to be mined.

[0060] (2) Radius of the inverted cone layer in the direction of the Kth layer directional angle θ

[0061]

[0062] (3) Conversion of grid points to polar coordinates

[0063] θ ij =atan2(y j -y0, x i -x0)

[0064] Note: Set the grid center (x) i ,y i The expression is transformed into (ρ,θ) with the center point (x0,y0) as the pole.

[0065]

[0066] If a point lies within a closed curve (inverted floating cone section), it is a valid block; the set Ω represents all valid blocks.

[0067] (4) Absolute index to relative index (for easier template / mask operations)

[0068] Δn(i,j,k)=(i-i0,j-j0,k-k0),

[0069] It is a discrete inverted floating cone model (a set of relative indices with the central block as the origin), used for efficient exclusion and neighborhood operations.

[0070] Step 4: Generate the final optimized state.

[0071] By using the discrete inverted cone model, initial block boundaries, and economic valuation information to implement inverted cone elimination, a final mining boundary is obtained that satisfies multi-directional slope angle constraints and achieves relatively optimal economic value, thus forming a block-based boundary optimization result.

[0072] Analysis of the effect of this embodiment:

[0073] Assuming the current coal market price is 800 yuan / ton and the stripping cost is 8 yuan / ton·meter, the economic value of each block can be calculated using the formula mentioned earlier. Combining these blocks with economic attributes with the initial boundary creates an initial economic value block boundary model, providing basic data support for subsequent inverted cone elimination and final boundary optimization. Figure 3 As shown.

[0074] Based on the geological conditions in different directions of the mining area, the slope angles in the east, south, west, and north directions are 10°, 20°, 10°, and 15°, respectively. To avoid confusion, this embodiment specifies that slope angles are expressed in degrees, while direction angles are expressed in radians. Using the aforementioned direction angles and corresponding slope angles as inputs to the Hermite curve, the difference curve between direction angle and slope angle can be obtained. Based on this difference curve, and combined with the predicted maximum mining depth of 516 m (divided into 43 layers, each 12 m high), the cover area of ​​the lowest layer can be determined. Furthermore, during the layer-by-layer traversal, the cover area within each layer can be determined similarly using the difference curve, thus forming a layered block division result. Figure 4 As shown.

[0075] Using the difference curve distribution generated in the previous step, each layer of blocks is effectively labeled along the Z-axis to generate a discretized inverted cone model (e.g., Figure 5 This discrete model not only preserves the geometric shape under multi-directional slope angle constraints, but also facilitates subsequent fast mask operations based on relative indices and elimination of inverted floating cones, thereby improving the computational efficiency and controllability of boundary optimization.

[0076] By using a discrete inverted cone model and initial block boundaries to eliminate inverted cones, the final optimized boundary is obtained, such as... Figure 6 As shown.

[0077] The polar coordinate discretized inverted cone exclusion model ensures sufficient constraints on slope angles in all directions during boundary optimization, thereby guaranteeing that the final boundary meets engineering safety requirements. Discretization using polar coordinates not only reduces data redundancy and improves model efficiency in a computing cluster environment, but also facilitates parallelization and batch computation of the optimization process. Furthermore, the model organically combines slope angle constraints with economic estimation, ensuring that the optimized mining boundary maximizes economic benefits while maintaining safety and feasibility, resulting in an economically optimal boundary scheme that aligns with engineering realities.

[0078] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for optimizing the boundary of an inverted floating cone based on polar coordinate discretization, characterized in that, Includes the following steps: S1, Initial boundary for generating block values: Based on the preset coal price and block burial depth, the coal-rock ratio in the initial boundary model is converted into economic value, and an initial block model based on economic value is established. S2, Fitting the slope angle difference curve: In the polar coordinate system, according to the slope angle parameters corresponding to different directions in the mining area, the interpolation function is used to fit the discrete direction angle-slope angle point set to generate a continuous direction angle-slope angle difference curve. S3. Based on the difference curve and the maximum mining depth, determine the overall geometric shape of the block; combine the difference curve and the layer height parameter to generate closed curves that divide the inside and outside of the block in each layer; by traversing layer by layer along the mining depth direction, obtain the effective blocks on each plane, and convert the absolute index of the effective blocks into a relative index relative to the central block to construct a discrete inverted cone model based on polar coordinates. S4. The discrete inverted cone model is used to remove the inverted cone from the initial block boundary to obtain the final mining boundary that satisfies the multi-directional slope angle constraints and optimizes economic value.

2. The method for optimizing the boundary of an inverted floating cone based on polar coordinate discretization according to claim 1, characterized in that, The process of establishing an initial block model based on economic value as described in step S1 specifically includes: S11, provides Q, which includes the quantity of block coal. i Block stripping ratio λ i and the burial depth d of the block i The initial level model of information; S12, based on the preset coal price P c Unit stripping cost C s and depth-related cost function f(d) i ), calculate the economic value Vi of each block, using the following formula: V i =Q i ·P c -[Q i ·(1+λ i )]·C s -f(d i ) In the formula, Q i ·P c This represents the revenue from bulk coal resources; (Q) i ·λ i )·C s f(d) represents the stripping cost corresponding to the amount of coal; i ) represents the additional cost or reduction function related to depth; S13, assign a corresponding economic value V to each block in the initial boundary model. i Thus, the initial block model based on economic value is established.

3. The inverted floating cone boundary optimization method based on polar coordinate discretization according to claim 1, characterized in that, Step S2, which involves fitting the discrete direction angle-slope angle point set using an interpolation function, specifically includes: S21, Obtain a discrete set of points consisting of multiple orientation angle-slope angle data pairs, where each data pair includes an orientation angle and its corresponding design slope angle; S22, assign the derivative value to zero for each data point in the discrete point set to satisfy the conservative value selection principle of slope design; S23, using the discrete point set and the derivative value corresponding to each data point as input, a piecewise polynomial function is constructed as the difference curve using the Hermite interpolation method; wherein, for each data point in the discrete point set, the function value of the difference curve at that point is equal to the given design slope angle, and the derivative value at that point is equal to the given zero value. S24, output the difference curve to determine the slope angle under any direction angle.

4. The inverted floating cone boundary optimization method based on polar coordinate discretization according to claim 1, characterized in that, Determining the geometric shape of the overall block as described in step S3 includes the following steps: Define an inverted conical geometric boundary in three-dimensional space, constrained by the difference curve and the maximum mining depth; The geometric boundary is constructed in the following layered manner: the maximum mining depth range is divided into multiple horizontal layers according to a preset layer height. For each depth layer, a contour radius that varies with the direction angle on the horizontal plane is calculated based on the depth value of the layer and the difference curve. The geometric shape of the overall block is the closed volume defined in three-dimensional space by the contour radii corresponding to all depth layers and varying with the direction angle.

5. The inverted floating cone boundary optimization method based on polar coordinate discretization according to claim 1, characterized in that, The method for obtaining the effective blocks on each plane in step S3 is as follows: for any block to be judged located in the layer, its horizontal position is converted to polar coordinates with the center of the cone as the pole to obtain its polar radius and direction angle; if the polar radius of the block is not greater than the contour radius corresponding to the direction angle, then the block is determined to be within the boundary of the geometric shape.

6. The inverted floating cone boundary optimization method based on polar coordinate discretization according to claim 1, characterized in that, The construction of the discrete inverted floating cone model based on polar coordinates in step S3 refers to converting the absolute spatial index of all the blocks that are determined to be valid into relative index offsets relative to the predefined center block index of the inverted floating cone. The set of relative index offsets constitutes the discrete inverted floating cone model, which is used for mask matching and neighborhood calculation in the subsequent inverted floating cone elimination process.

7. The method for optimizing the boundary of an inverted floating cone based on polar coordinate discretization according to claim 1, characterized in that, Step 4, which refers to generating the final optimized state, means: Calculate the total economic value of all blocks in the set of valid blocks; Determine whether the total economic value is less than or equal to zero; If the total economic value is less than or equal to zero, the set of valid blocks is excluded from the initial block boundary to update the boundary.

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