Mining subsidence prediction parameter solving method based on improved center collision optimization algorithm

Abstract

The invention discloses a mining subsidence prediction parameter solving method based on an improved center collision optimization algorithm, and belongs to the field of mine deformation monitoring data processing. Aiming at the defects that a basic center collision optimization algorithm is prone to premature convergence and insufficient in optimization precision when solving a mining subsidence parameter inversion problem, a Huber loss function is adopted to construct a fitness evaluation model to enhance the robust capability of the algorithm, and Cubic mapping is utilized to generate a random number to improve the stability of a search process, so that the method is suitable for the mining subsidence parameter inversion problem. And a self-adaptive elite-guided Cauchy variation mechanism is introduced to enhance the global exploration capability. According to the method, firstly, a probability integral method parameter inversion problem is constructed into an optimization model, and a population is initialized; performing double-space collaborative search in an original space and a decorrelation space constructed based on principal component analysis, and iteratively updating a population in combination with a dynamic space allocation strategy; and finally outputting an optimal parameter solution. According to the method, the convergence precision, stability and robustness of the algorithm in complex nonlinear parameter inversion are effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of mine deformation monitoring data processing, specifically involving a method for solving mining subsidence prediction parameters based on an improved center collision optimization algorithm. Background Technology

[0002] The theory of mining subsidence prediction plays a crucial role in guiding mining operations under buildings, railways, and water bodies, assessing potential geological hazards, and analyzing the subsidence mechanism of mining areas. The probability integral method is the officially designated method for mining subsidence prediction in China. Traditional probability integral method parameter inversion methods mainly include the characteristic point method, the linear approximation method, and the orthogonal experimental method. The characteristic point method suffers from large parameter calculation errors due to the difficulty in accurately determining the characteristic points of the curve. The linear approximation method mainly includes the least squares iterative method, the Gauss-Newton method, and the steepest descent method. Although the linear approximation method has a rigorous parameter calculation theory and high accuracy, the parameter model is a complex nonlinear function, and some probability integral parameters are correlated. This makes the linear approximation method extremely demanding on the layout of the surface mobile observation station and the accuracy of the initial values ​​of the parameter model (low accuracy of the initial parameters easily leads to divergence of the parameter model), making its engineering application still quite difficult. While the orthogonal experimental method effectively solves the problems of parameter calculation failure due to arbitrary working face shapes and unreasonable initial value selection, it suffers from drawbacks such as a large number of experiments, slow parameter calculation speed, and difficulty in computer implementation. In recent years, intelligent optimization methods such as genetic algorithms and particle swarm optimization have been introduced into this field, which have improved the solution effect to some extent. However, due to the complexity of the probability integral parameter search space and the existence of multiple local extrema, these algorithms are prone to problems such as premature convergence and getting trapped in local optima during the solution process, resulting in large fluctuations in the parameter inversion results and difficulty in ensuring stable solution accuracy. Therefore, existing technologies have problems with insufficient convergence accuracy and robustness in mining subsidence parameter inversion. Summary of the Invention

[0003] To address the problems of premature convergence, local optima, and insufficient accuracy and robustness in existing mining subsidence parameter inversion methods, the present invention aims to provide a mining subsidence prediction parameter solution method based on an improved center collision optimization algorithm.

[0004] The objective of this invention can be achieved through the following technical solutions: A method for solving mining subsidence prediction parameters based on an improved center collision optimization algorithm includes the following steps: S1. Determine the parameter vector to be determined by the probability integral method, and preset the corresponding value range for each parameter. Based on the value range, randomly generate an initial pedestrian population, with each individual pedestrian representing a parameter vector. S2. Obtain the location information of various surface monitoring points on the mining face, and calculate the expected subsidence value of each monitoring point based on the parameter vector represented by each individual pedestrian using the probability integral method. S3. Obtain the measured subsidence values ​​of various surface monitoring points on the mining face, and calculate the fitness of each individual pedestrian in combination with the predicted subsidence values; S4. Set a termination condition and iteratively update the pedestrian population with the goal of minimizing fitness. The iterative update process includes: based on the group interaction behavior of the pedestrian population, generating pedestrian individuals representing new parameter vectors through three stages: constructing a dual search space, execution center collision interaction, and adaptive elite mutation, and calculating the fitness of the corresponding pedestrian individuals; at the same time, selecting the next generation population from the current population through a preset selection mechanism. S5. When the iteration termination condition is met, output the parameter vector represented by the pedestrian individual with the minimum fitness in the next generation population, and use it as the final mining subsidence prediction parameter.

[0005] Furthermore, in step S3, the fitness is calculated using a robust estimation method based on the Huber loss function, and the specific formula is as follows: For the i-th pedestrian individual, the fitness calculation formula is:

[0006] in, The residual at the j-th monitoring point; Here is the Huber loss function. It is defined as:

[0007] in, This is the preset robustness threshold.

[0008] Furthermore, the construction of the dual search space specifically includes the following steps: 1. Original space: The original domain space of the parameters is maintained; 2. Relevance Space: Constructed based on the distribution characteristics of a subset of poorly fit individuals in the current population using principal component analysis; 3. The specific construction method is as follows: after selecting the fitness ranking... For individuals of a certain proportion, calculate their mean vector. Covariance Matrix ;right Eigenvalue decomposition yields the eigenvector matrix. (Sort by eigenvalues ​​in descending order); then retrieve the coordinates in the relevant space. Compared with the original spatial coordinates The transformation relationship is as follows: .

[0009] Furthermore, the collision interaction of the execution center specifically includes the following steps: For the current individual Updates are performed based on whether the data is randomly assigned to the original space (OS) or to the relevant space (DS): If updating in the original space: 1. Select four reference individuals from the set of individuals with better fitness than the current individual. ; 2. Randomly select two individuals from the entire population. ; 3. Calculate dynamic parameters ,in This represents the current iteration number. This represents the maximum number of iterations. 4. Generate random numbers and dimension mask vector ,in Each component is composed of random numbers and Comparison and decision: The random number here Through Cubic mapping Generating random number sequences to improve their uniformity and stability; 5. Calculate the mixture vector ; 6. Update location: ,in This indicates element-wise multiplication.

[0010] If you need to update the relevant space: 1. Map the current individual to the decorrelational space: ; 2. In the relevant space, following the same center collision rules as the original space (steps 1-6), calculate the new position using the transformed coordinates. ; 3. Transform the new position back to the original space: .

[0011] Furthermore, the adaptive elite mutation specifically includes the following steps: 1. Set the mutation probability that decays with iteration. and variation scale ; 2. For each newly generated individual With probability Execute Cauchy mutation: ,in As the current globally optimal individual, A random vector generated by the Cubic mapping; 3. Calculation If its fitness is better than Then use replace .

[0012] Furthermore, the iterative update process also includes dynamically adjusting the dual-space allocation ratio, as follows: 1. Let the proportion of individuals allocated to the decorrelation space (DS) for updates in the current iteration be . The original space (OS) ratio is ; 2. Calculate the proportion of individuals successfully updated (i.e., the new individuals have better fitness) in DS and OS respectively, out of the total number of individuals allocated in each, and denote it as . and ; 3. The next-generation allocation ratio to DS has been updated as follows: And constrained to preset upper and lower limits. Inside.

[0013] Furthermore, the selection of the next generation population from the current population according to the preset selection mechanism specifically includes the following steps: 1. Merge the population of new pedestrians generated after central collision interaction and adaptive elite mutation with the parent population. 2. Through the elite preservation strategy, the individual with the lowest fitness in the merged population is retained as an elite individual and directly enters the next generation; 3. For the remaining individuals, a tournament selection method based on fitness ranking is adopted. Several individuals are randomly selected each time, and the one with the best fitness is retained. This process is repeated until a specified number of individuals are selected to form the next generation population. 4. At the same time, an early stopping mechanism is set: if the improvement of the global optimal fitness value is less than the preset tolerance for multiple consecutive generations, early stopping is triggered and the current optimal solution is output.

[0014] Furthermore, the parameter vector to be determined by the probability integral method ,in This is the subsidence coefficient; To influence the tangent angle; The angle of propagation of the impact of mining; This is the inflection point offset distance parameter; used to describe the asymmetric deformation characteristics of subsidence basins.

[0015] The beneficial effects of this invention are: This application constructs a three-stage system—dual search space construction, center collision interaction, and adaptive elite mutation—to efficiently search the parameter space by simulating the interaction and pathfinding behavior of pedestrian groups in complex environments. The dual search space mechanism (original space and decorrelational space) enables parallel exploration and collaborative development of different characteristic regions of the parameter space; the center collision interaction mechanism balances the algorithm's convergence speed and exploration capability by utilizing the guidance of dominant individuals and random interference; and the adaptive elite mutation mechanism significantly enhances the algorithm's ability to escape local optima by introducing controllable Cauchy perturbations. The three stages work synergistically, supplemented by improvements such as the Huber robust loss function and Cubic mapping random number generation, effectively overcoming the problems of premature convergence, getting trapped in local optima, and sensitivity to data noise in existing algorithms for mining subsidence parameter inversion. This significantly improves the convergence accuracy, solution stability, and robustness of the algorithm. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a schematic diagram of the overall process of the present invention; Figure 2 This is a schematic diagram showing the distribution of the working surfaces in an embodiment of the present invention; Figure 3 This is a schematic diagram of the settlement of the directional line in an embodiment of the present invention; Figure 4 This is a schematic diagram of the settlement of the inclined line in an embodiment of the present invention; Figure 5 This is a two-dimensional sedimentation comparison diagram in an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] like Figures 1 to 5 As shown, a method for solving mining subsidence prediction parameters based on an improved center collision optimization algorithm includes the following steps: Determine the parameter vector to be solved by the probability integral method, and preset the corresponding value range for each parameter. Based on the value range, randomly generate an initial pedestrian population, with each individual pedestrian representing a parameter vector. The location information of various surface monitoring points on the mining face is obtained, and the expected subsidence value of each monitoring point is calculated by probability integration based on the parameter vector represented by each individual pedestrian. The measured subsidence values ​​at various surface monitoring points on the mining face were obtained, and the fitness of each individual pedestrian was calculated in combination with the predicted subsidence values. The system has a preset termination condition and aims to minimize the fitness of pedestrians. The iterative update process includes generating pedestrian individuals representing new parameter vectors by constructing a dual search space, execution center collision interaction, and adaptive elite mutation based on fitness, and calculating the fitness of the corresponding pedestrian individuals. At the same time, a preset selection mechanism selects the next generation of the population from the current population. When the iteration termination condition is met, the parameter vector represented by the pedestrian individual with the minimum fitness in the next generation population is output and used as the final mining subsidence prediction parameter.

[0020] Preferably, the termination condition is to output the optimal parameter solution when the preset maximum number of iterations is reached, a solution that meets the accuracy requirements is found and the solution is not improved in a certain number of subsequent iterations, or the adaptive restart mechanism has reached the maximum number of restarts.

[0021] This application constructs a dual search space, performs center collision interaction, and adaptive elite mutation, and selects the next generation from the current population using a preset selection mechanism to iteratively optimize and update the pedestrian population. The dual search space construction enables collaborative parallel search of the original space and the decorrelation space. Center collision interaction utilizes dominant individuals to guide exploration and development while balancing random disturbances. Adaptive elite mutation enhances the algorithm's ability to escape local optima by introducing controllable Cauchy perturbations. The synergistic effect of these three elements effectively overcomes the problems of premature convergence and getting trapped in local optima in existing algorithms, improving the convergence accuracy, solution stability, and robustness of the solution for mining subsidence prediction parameters.

[0022] The construction of a dual search space based on fitness includes the following steps: 1. Retain the original parameter domain as the original space; 2. Based on the distribution characteristics of a subset of individuals with poor fitness in the current population (such as the bottom 50% of individuals by fitness ranking), a decorrelation space is constructed using principal component analysis; 3. The specific method is as follows: Calculate the mean vector of the selected poorest individuals. Covariance Matrix ;right Perform eigenvalue decomposition to obtain an eigenvector matrix arranged in descending order of eigenvalues. Then retrieve the coordinates in the relevant space. Compared with the original spatial coordinates The transformation relationship is as follows: .

[0023] Based on the constructed dual search space, a center collision interaction is performed to generate new candidate solutions, specifically including the following steps: For the current individual Update it based on whether it is assigned to the original space or to the relevant space: If updating in the original space: 1. Select four reference individuals from the set of individuals with better fitness than the current individual. ; 2. Randomly select two individuals from the entire population. ; 3. Calculate dynamic parameters ,in This represents the current iteration number. This represents the maximum number of iterations. 4. Generate random numbers and dimension mask vector ,in Each component Random numbers generated by Cubic mapping and Comparison and decision: The Cubic mapping formula is: ,in The result is a uniformly random number in the range [0,1]. 5. Calculate the mixture vector ; 6. Update location: ,in This indicates element-wise multiplication.

[0024] If you need to update the relevant space: 1. Map the current individual to the decorrelational space: ; 2. In the relevant space, following the same center collision rules as the original space (steps 1-6), calculate the new position using the transformed coordinates. ; 3. Transform the new position back to the original space: .

[0025] Adaptive elite mutation is used to further enhance exploration capabilities after center collision interactions and to optimize newly generated individuals. Specifically, it includes the following steps: Set the mutation probability that decays with iteration. and variation scale ; For each newly generated individual With probability Execute Cauchy mutation: ,in As the current globally optimal individual, A random vector generated by the Cubic mapping; calculate If its fitness is better than Then use replace .

[0026] The updated parameter values ​​are subjected to boundary processing using the reflection mapping rule, as follows: like ,but ; like ,but ; in, express In the Values ​​in each parameter dimension; , They represent the first The theoretical lower bound and theoretical upper bound of each parameter.

[0027] The allocation ratio of the dual search space is dynamically adjusted according to the iteration process, as follows: Let the proportion of individuals assigned to the decorrelation space (DS) for updates in the current iteration be . The original space (OS) ratio is ; Calculate the proportion of individuals successfully updated (i.e., the new individuals have better fitness) in DS and OS respectively, out of the total number of individuals allocated in each, and denote it as . and ; The next generation allocation ratio to DS has been updated as follows: And constrained to preset upper and lower limits. Inside.

[0028] The selection of the next generation population from the current population according to a preset selection mechanism includes the following steps: The population of new pedestrians generated after the central collision interaction and adaptive elite mutation is merged with the initial pedestrian population. The selection mechanism combines elite retention strategies with tournament selection, as detailed below: The elite retention strategy preserves the pedestrian individual with the lowest fitness in the current population as the elite individual. The remaining pedestrians were selected using a tournament selection method. Each time, a random selection is made from the remaining individuals. For each individual, retain the one with the best fitness, and repeat this process until the selection is complete; Preferably, the number of pedestrian individuals in the initial population It is 50; At the same time, an early stopping mechanism is set: if the improvement of the global optimal fitness value is less than the preset tolerance for multiple consecutive generations, early stopping is triggered, and the current optimal solution is output.

[0029] The formula for calculating the fitness of individual pedestrians adopts a robust estimation method based on the Huber loss function, as follows:

[0030] in, The residual at the j-th monitoring point; The Huber loss function is defined as follows:

[0031] in, This is a preset robustness threshold, for example, a value of 0.01 (corresponding to 10mm).

[0032] The parameter vector to be determined by probability integral method ,in This is the subsidence coefficient; To influence the tangent angle; The angle of propagation of the impact of mining; The inflection point offset distance parameter is used to describe the asymmetric deformation characteristics of the subsidence basin.

[0033] The fluctuation range of each probability integral parameter is preset according to the specific geological and mining conditions.

[0034] In this invention, to verify the practical engineering application of the invention, the Zhuji Mine 1242(1) working face is taken as an example. The distribution of the working face is as follows: Figure 2 As shown, the working face adopts fully mechanized coal mining, mining the entire height in one pass, and managing the roof using the caving method. The geological and mining conditions of the working face are as follows: strike mining length 1628m, dip mining length 200m, average mining height 1.76m, and average coal seam dip angle. The main dip observation line is located approximately 1144m from the cut and 976m from the stop line, with a length of 1500m and 3 control points and 50 monitoring points, with a monitoring point spacing of 30m. The main strike observation line is located 39m off the working face centerline in the downhill direction, with a length of 3480m and 3 control points and 95 monitoring points, with a monitoring point spacing of 30 / 63m.

[0035] The observation station at the working face commenced connection measurements on December 6, 2021, and concluded on May 20, 2024, lasting approximately 29 months (896 days). The work included initial comprehensive observation, three routine observations, and eleven comprehensive observations. The horizontal connection measurement of the surface mobile observation station at the fully mechanized mining face utilized a Class D GPS network. Comprehensive observations during the mining process were conducted using GNSS, CORS, and RTK measurement standards for horizontal surveying; elevation measurements were performed using third-order geometric leveling; and patrol surveys and routine observations also employed third-order geometric leveling. The accuracy of the observation point subsidence and horizontal movement monitoring met engineering requirements.

[0036] Since the overlying strata in the mining area where the working face is located are of the weak type, the parameter fluctuation range is set as shown in Table 1. The center collision optimization algorithm and the improved center collision optimization algorithm were used to perform probability integral parameter inversion on the last observation data (the surface movement has entered a stable period) from the surface movement observation station at the working face. To avoid the randomness of the calculation results, 10 independent experimental calculations were performed, with each experiment repeated 10 times. The average value of the inversion parameters, the parameter mean error, and the root mean square of the subsidence fitting were calculated. The specific experimental results are shown in Table 1.

[0037] Table 1 Comparison of parameter calculation effects of CCO and ICCO ; As shown in Table 1: (1) From the perspective of parameter error, the ICCO inversion probability integral method parameters Mean error control within Within, inflection point offset distance The maximum mean error shall not exceed CCO inversion probability integral method parameters The mean error is controlled within Within, inflection point offset distance The maximum mean error shall not exceed This indicates that ICCO has better stability than CCO.

[0038] (2) In terms of fitting error, the fitting errors for the downward shift of the directional inversion parameters of CCO and ICCO are 17.513 and 17.273 mm, respectively, with ICCO showing a better fitting effect than CCO. The fitting effects for directional and dip subsidence are as follows: Figure 3 and Figure 4 As shown.

[0039] (3) The parameters of the Zhuji Mine 1242(1) working face obtained by ICCO inversion using the probability integral method are: Using the probabilistic integral method parameters obtained from ICCO inversion, and substituting them into the probabilistic integral method prediction model, the subsidence of the entire working face was predicted, and a two-dimensional comparison chart of the predicted subsidence at various points was plotted, as shown below. Figure 5 As shown.

[0040] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0041] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A method for solving mining subsidence prediction parameters based on an improved center collision optimization algorithm, characterized in that, Includes the following steps: Determine the parameter vector to be solved by the probability integral method, and preset the corresponding value range for each parameter. Based on the value range, randomly generate an initial pedestrian population, with each individual pedestrian representing a parameter vector. The location information of various surface monitoring points on the mining face is obtained, and the expected subsidence value of each monitoring point is calculated by probability integration based on the parameter vector represented by each individual pedestrian. The measured subsidence values ​​at various surface monitoring points on the mining face were obtained, and the fitness of each individual pedestrian was calculated in combination with the predicted subsidence values. The system has a preset termination condition and aims to minimize the fitness of pedestrians. The iterative update process includes generating pedestrian individuals representing new parameter vectors by searching the original space, searching the derelated space, and adaptive elite mutation based on fitness, and calculating the fitness of the corresponding pedestrian individuals. At the same time, a preset selection mechanism selects the next generation of the population from the current population. When the iteration termination condition is met, the parameter vector represented by the pedestrian individual with the minimum fitness in the next generation population is output and used as the final mining subsidence prediction parameter.

2. The method for solving mining subsidence prediction parameters based on the improved center collision optimization algorithm according to claim 1, characterized in that, The original space search and decorrelation space search in the iterative update process specifically include the following steps: Construct a decorrelation space transformation matrix based on the poorly fit individuals in the current population; A certain proportion of pedestrians are dynamically allocated to the original space for updating, and the remaining individuals are mapped to the relevant space for updating. In the original space, the updated position of an individual pedestrian is determined by the individual with better fitness, the randomly selected individual, and dynamic parameters. In the relevant space, the updated position of an individual pedestrian is determined by the same rules after spatial transformation, and then the position is reversed back to the original space after the update.

3. The method for solving mining subsidence prediction parameters based on the improved center collision optimization algorithm according to claim 2, characterized in that, The position update formula in the original space or the relevant space is as follows: ； in, A reference individual is selected from the set of individuals with better fitness than the current individual; A combination of random numbers and dynamic parameters The generated binary vectors are compared to control how each parameter dimension is updated; This is a mixed vector, generated by a linear combination of multiple reference individuals and a random individual, specifically expressed as: ； in, Other reference individuals selected from those with high fitness; Individuals randomly selected from the population; For the current individual; These are dynamic parameters; It is a random number within the interval [0,1].

4. The method for solving mining subsidence prediction parameters based on the improved center collision optimization algorithm according to claim 3, characterized in that, The dynamic parameters The calculation formula is as follows: ； in, This represents the current iteration number; This represents the total number of iterations.

5. The method for solving mining subsidence prediction parameters based on the improved center collision optimization algorithm according to claim 1, characterized in that, The fitness of each individual pedestrian is calculated using a robust estimation method based on the Huber loss function, and the specific calculation formula is as follows: ； in, This represents the residual between the predicted settlement value and the measured settlement value. The preset threshold parameter; individual fitness This is the sum of Huber losses for the residuals at all monitoring points.

6. The method for solving mining subsidence prediction parameters based on the improved center collision optimization algorithm according to claim 1, characterized in that, The iterative update process uses Cubic mapping to generate random numbers, which are used to initialize the population and for random selection during the update process. The mapping formula is as follows: ； in, is a random number uniformly distributed in the interval [0,1]. These are random numbers transformed by the Cubic mapping.

7. The method for solving mining subsidence prediction parameters based on the improved center collision optimization algorithm according to claim 1, characterized in that, The adaptive elite mutation specifically includes the following steps: Preset a mutation probability that decays with the number of iterations. and variation scale ; After each position update, with probability The newly generated individuals undergo elite-guided Cauchy mutation; the mutation formula is: ； in, It is the currently globally optimal individual; , For the parameter boundary vector; The numbers are uniformly random numbers in the interval [0,1]. The fitness of the mutated individuals is compared with that of the original updated individuals, and the better ones are retained.

8. The method for solving mining subsidence prediction parameters based on the improved center collision optimization algorithm according to claim 1, characterized in that, The ratio of individuals searched in the original space to the decorrelation space is dynamically allocated using an adaptive adjustment strategy based on search success rate, as follows: Calculate the proportion of individuals that were successfully updated in the decorrelation space (DS) in the current iteration. and the proportion of individuals successfully updated in the original space (OS). ; The proportion of individuals allocated to relevant spaces in the next generation Updated to: And constrained to preset upper and lower limits. Inside; The proportion allocated to the original space is .

9. The method for solving mining subsidence prediction parameters based on the improved center collision optimization algorithm according to claim 1, characterized in that, The parameter vector to be determined by the probability integral method ,in This is the subsidence coefficient; To influence the tangent angle; The angle of propagation is affected by mining operations; This is the inflection point offset distance parameter.

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