A method, apparatus, and electronic equipment for optimizing the reliability of hydraulic supports.

Abstract

This invention discloses a reliability optimization method, apparatus, and electronic device for hydraulic supports, relating to the field of hydraulic support technology, which can reduce computational costs and improve reliability optimization efficiency. The method includes: obtaining an initial sample set for the hydraulic support; constructing a radial basis function surrogate model based on the initial sample set, wherein the radial basis function surrogate model consists of k radial basis functions, each corresponding to a center point and a width parameter; optimizing the center point and the width parameter using a fungal growth optimization algorithm; and constructing the radial basis function surrogate model based on the optimized center point and the width parameter, where k is less than N; and performing reliability optimization on the hydraulic support based on the radial basis function surrogate model. This invention is applicable to the reliability optimization of hydraulic supports.

Description

Technical Field

[0001] This invention relates to the field of hydraulic support technology, and in particular to a method, apparatus, electronic device, and storage medium for optimizing the reliability of hydraulic supports. Background Technology

[0002] In structural optimization design, traditional deterministic optimization methods struggle to guarantee the stability and safety of structures under various uncertainties (such as material property fluctuations, processing errors, and load randomness). Reliability optimization design methods, by introducing probabilistic constraints or failure probability assessments, comprehensively consider the uncertainties of random variables, effectively improving the reliability of structures in uncertain environments. However, in reliability optimization design, taking Monte Carlo Simulation (MCS) as an example, this method requires calculating response values ​​for a large number of sample points, typically necessitating the use of finite element simulation and other methods to obtain these values, resulting in high computational costs and low efficiency. Summary of the Invention

[0003] In view of this, embodiments of the present invention provide a method, apparatus, electronic device and storage medium for optimizing the reliability of hydraulic supports, which can reduce computing costs and improve the efficiency of reliability optimization.

[0004] In a first aspect, embodiments of the present invention provide a reliability optimization method for a hydraulic support, the method comprising: obtaining an initial sample set of the hydraulic support, the initial sample set containing at least N samples, each sample including design parameters of a first force-bearing component of the hydraulic support, and a target response value and a limit response value corresponding to the design parameters, wherein N is a positive integer, the design parameters are d-dimensional vectors, and d is a positive integer; constructing a radial basis function surrogate model based on the initial sample set, wherein the radial basis function surrogate model consists of k radial basis functions, each radial basis function corresponding to a center point and a width parameter, optimizing the center point and the width parameter using a fungal growth optimization algorithm, and constructing the radial basis function surrogate model based on the optimized center point and the width parameter, wherein k is less than N; and optimizing the reliability of the hydraulic support based on the radial basis function surrogate model.

[0005] In one embodiment, the radial basis function surrogate model includes an objective function sub-model and a limit state sub-model, wherein the objective function sub-model is used to determine the mapping relationship between the design parameters and the mass of the first load-bearing component of the hydraulic support, and the limit state sub-model is used to determine the mapping relationship between the design parameters and the maximum stress of the first load-bearing component of the hydraulic support.

[0006] In one embodiment, each mycelium in the fungal growth optimization algorithm is encoded as a vector with dimensions k×d+k, wherein each mycelium contains center points and width parameters corresponding to k radial basis functions, each center point is a d-dimensional vector, and each width parameter is a scalar.

[0007] In one embodiment, constructing a radial basis function surrogate model based on the initial sample set includes: encoding the k centroids and k width parameters as mycelia based on the initial sample set; using the root mean square error between the predicted value of the objective function sub-model and the true value in the initial sample set, and the root mean square error between the predicted value of the limiting state sub-model and the true value in the initial sample set, respectively, as fitness indices, obtaining preferred mycelia through regional differential growth iteration of a fungal growth optimization algorithm, and determining preferred centroids and preferred width parameters, wherein the regional differential includes eutrophic regions or hypotrophic regions, the fitness index corresponding to the eutrophic region is less than a preset threshold, and the fitness value corresponding to the hypotrophic region is greater than or equal to a preset threshold; and determining a preferred radial basis function surrogate model based on the preferred centroids and preferred width parameters.

[0008] In one embodiment, after determining the preferred radial basis function surrogate model based on the preferred center point and the width parameter, and before performing reliability optimization on the hydraulic support based on the radial basis function surrogate model, the method further includes: based on the radial basis function surrogate model, with the goal of improving the prediction accuracy of the model near the limit state surface, and in conjunction with dynamic distance constraints, searching for new sample points within a preset distance range from the limit state surface, wherein the limit state surface is a continuous surface formed by the design parameter vectors whose predicted values ​​of the limit state sub-model are equal to zero; performing finite element simulation on the new sample points to obtain the corresponding target response value and limit response value, and combining the new sample points and... The corresponding target response value and the limit response value are added to the sample set as a new sample; the radial basis function surrogate model is retrained based on the updated sample set to obtain a corresponding preferred radial basis function surrogate model. The process then jumps to the step of searching for new sample points within a preset distance range from the limit state surface based on the radial basis function surrogate model, with the goal of improving the prediction accuracy of the model near the limit state surface, combined with dynamic distance constraints. The step of searching for new sample points within a preset distance range from the limit state surface, where the limit state surface is the continuous surface formed by the design parameter vectors whose predicted values ​​of the limit state sub-model are equal to zero, continues to be executed. This process is iterated until the model accuracy meets the preset stopping criterion, resulting in the updated preferred radial basis function surrogate model.

[0009] In one implementation, the threshold of the dynamic distance constraint is used to control the minimum distance between new sample points and existing sample points.

[0010] In one implementation, the preset stopping criterion is that the average rate of change of the determination coefficient of the limit state sub-model is less than a preset threshold in three consecutive iterations.

[0011] In one implementation, the reliability optimization of the hydraulic support based on the radial basis function surrogate model includes: transforming the design parameters of the hydraulic support to a standard normal space, initializing the estimated value of the most likely failure point as the mean point of the design parameters, and initializing the constraint offset to zero, wherein the most likely failure point is the point that satisfies the condition that the limit state sub-model predicts a value of zero and has the highest probability density; performing deterministic optimization on the radial basis function surrogate model with the objective of minimizing the mass predicted by the objective function sub-model and with the constraint that the stress margin predicted by the limit state sub-model plus the constraint offset is greater than or equal to zero, to obtain candidate design points; for the candidate design points, generating multiple sample points through Monte Carlo simulation according to the preset random distribution of the design parameters, predicting the limit state function value of each sample using the limit state sub-model, and statistically analyzing the proportion of samples with limit state function values ​​less than zero as the failure probability to determine the candidate design points. The reliability of the candidate design point is determined. If the reliability of the candidate design point does not meet the preset target reliability, the most likely failure point corresponding to the candidate design point is determined in the standard normal space, and the constraint offset is updated according to the difference between the target reliability index and the reliability index corresponding to the current most likely failure point. The most likely failure point is added to the sample set, the sample set is updated, and the radial basis function surrogate model is retrained. The process jumps to the step of performing deterministic optimization on the radial basis function surrogate model with the objective of minimizing the quality predicted by the objective function sub-model and the constraint that the stress margin predicted by the limit state sub-model plus the constraint offset is greater than or equal to zero. The process continues to execute the step of obtaining the candidate design point. The iteration continues until the rate of change of the objective function value obtained by the deterministic optimization for M consecutive times is less than the preset threshold, and the reliability of the candidate design point meets the preset reliability. The candidate design point is then output as the final optimization result, where the value of M ranges from 2 to 6.

[0012] In one implementation, the number k of the radial basis functions is determined according to the dimension d of the design parameters.

[0013] In one embodiment, obtaining the initial sample set of the hydraulic support includes: generating initial design samples of the hydraulic support using Latin hypercube sampling; performing finite element simulation of the hydraulic support on each set of samples to obtain the mass response value and maximum stress response value of the first stress-bearing component corresponding to each set of samples, and constructing the initial sample set.

[0014] In one embodiment, the first load-bearing component of the hydraulic support includes a top beam or a base.

[0015] In one embodiment, the first load-bearing component is a symmetrical three-chamber box-shaped structure, and the design parameters include the thickness of the top cover plate, the thickness of the bottom plate, the thickness of the stiffening ribs, the thickness of the side plates, the half-spacing of the stiffening ribs, the width of the box, and the thickness of the box.

[0016] Secondly, embodiments of the present invention also provide a reliability optimization device for a hydraulic support, the device comprising: an acquisition unit, configured to acquire an initial sample set of the hydraulic support, the initial sample set containing at least N samples, each sample including design parameters of a first force-bearing component of the hydraulic support, and a target response value and a limit response value corresponding to the design parameters, wherein N is a positive integer, the design parameters are d-dimensional vectors, and d is a positive integer; a construction unit, configured to construct a radial basis function surrogate model based on the initial sample set, wherein the radial basis function surrogate model consists of k radial basis functions, each radial basis function corresponding to a center point and a width parameter, the center point and the width parameter are optimized using a fungal growth optimization algorithm, and the radial basis function surrogate model is constructed based on the optimized center point and the width parameter, wherein k is less than N; and an optimization unit, configured to perform reliability optimization on the hydraulic support based on the radial basis function surrogate model.

[0017] In one embodiment, the radial basis function surrogate model includes an objective function sub-model and a limit state sub-model, wherein the objective function sub-model is used to determine the mapping relationship between the design parameters and the mass of the first load-bearing component of the hydraulic support, and the limit state sub-model is used to determine the mapping relationship between the design parameters and the maximum stress of the first load-bearing component of the hydraulic support.

[0018] In one embodiment, each mycelium in the fungal growth optimization algorithm is encoded as a vector with dimensions k×d+k, wherein each mycelium contains center points and width parameters corresponding to k radial basis functions, each center point is a d-dimensional vector, and each width parameter is a scalar.

[0019] In one embodiment, the construction unit is specifically used to: encode the k centroids and k width parameters into mycelia based on the initial sample set; using the root mean square error between the predicted value of the objective function sub-model and the true value in the initial sample set, and the root mean square error between the predicted value of the limiting state sub-model and the true value in the initial sample set, respectively, as fitness indices, and through regional differential growth iteration of a fungal growth optimization algorithm, obtain preferred mycelia, and determine preferred centroids and preferred width parameters, wherein the regional differentiation includes eutrophic regions or hypotrophic regions, the fitness index corresponding to the eutrophic region is less than a preset threshold, and the fitness value corresponding to the hypotrophic region is greater than or equal to a preset threshold; and determine a preferred radial basis function surrogate model based on the preferred centroids and preferred width parameters.

[0020] In one embodiment, the device further includes: a search unit, configured to, after the construction unit determines the preferred radial basis function surrogate model and before the reliability optimization of the hydraulic support based on the radial basis function surrogate model, search for new sample points within a preset distance range from the limit state surface, with the goal of improving the prediction accuracy of the model near the limit state surface, combined with dynamic distance constraints, wherein the limit state surface is a continuous surface composed of the design parameter vectors whose predicted values ​​of the limit state sub-model are equal to zero; a simulation unit, configured to perform finite element simulation on the new sample points, obtain the corresponding target response value and limit response value, and add the new sample point and its corresponding target response value and limit response value as a new sample to the sample set; a training unit, configured to retrain the radial basis function surrogate model based on the updated sample set to obtain a corresponding preferred radial basis function surrogate model; and a triggering unit, configured to trigger the search unit to continue execution, iterating cyclically until the model accuracy meets a preset stopping criterion, thereby obtaining the updated preferred radial basis function surrogate model.

[0021] In one implementation, the threshold of the dynamic distance constraint is used to control the minimum distance between new sample points and existing sample points.

[0022] In one implementation, the preset stopping criterion is that the average rate of change of the determination coefficient of the limit state sub-model is less than a preset threshold in three consecutive iterations.

[0023] In one embodiment, the optimization unit includes: a transformation module, configured to transform the design parameters of the hydraulic support to a standard normal space, initialize the estimated value of the most likely failure point as the mean point of the design parameters, and initialize the constraint offset to zero, wherein the most likely failure point is the point that satisfies the condition that the predicted value of the limit state sub-model is zero and has the highest probability density; a deterministic optimization module, configured to perform deterministic optimization on the radial basis function surrogate model with the objective of minimizing the quality predicted by the objective function sub-model and with the constraint that the stress margin predicted by the limit state sub-model plus the constraint offset is greater than or equal to zero, to obtain candidate design points; and a Monte Carlo module, configured to generate multiple sample points for the candidate design points through Monte Carlo simulation based on a preset random distribution of the design parameters, and predict the limit state function of each sample using the limit state sub-model. The reliability of the candidate design point is determined by the proportion of samples with a limit state function value less than zero as the failure probability. An update module is used to determine the most likely failure point corresponding to the candidate design point in the standard normal space if the reliability of the candidate design point does not meet the preset target reliability. The constraint offset is updated based on the difference between the target reliability index and the reliability index corresponding to the current most likely failure point. A retraining module adds the most likely failure point to the sample set, updates the sample set, and retrains the radial basis function surrogate model. This triggers the deterministic optimization module to continue execution, iterating until the rate of change of the objective function value obtained from M consecutive deterministic optimizations is less than a preset threshold, and the reliability of the candidate design point meets the preset reliability. The candidate design point is then output as the final optimization result, where M ranges from 2 to 6.

[0024] In one implementation, the number k of the radial basis functions is determined according to the dimension d of the design parameters.

[0025] In one embodiment, the acquisition unit is specifically used to: generate initial design samples of the hydraulic support using Latin hypercube sampling; perform finite element simulation of the hydraulic support on each set of samples, obtain the mass response value and maximum stress response value of the first stress-bearing component corresponding to each set of samples, and construct the initial sample set.

[0026] In one embodiment, the first load-bearing component of the hydraulic support includes a top beam or a base.

[0027] In one embodiment, the first load-bearing component is a symmetrical three-chamber box-shaped structure, and the design parameters include the thickness of the top cover plate, the thickness of the bottom plate, the thickness of the stiffening ribs, the thickness of the side plates, the half-spacing of the stiffening ribs, the width of the box, and the thickness of the box.

[0028] Thirdly, embodiments of the present invention also provide an electronic device, the electronic device comprising: a processor and a memory, the processor being electrically connected to the memory; the memory being used to store executable program code; the processor running a program corresponding to the executable program code by reading the executable program code stored in the memory, thereby implementing the reliability optimization method for hydraulic supports provided in any one of the embodiments of the present invention.

[0029] Fourthly, embodiments of the present invention also provide a computer-readable storage medium storing one or more programs that can be executed by one or more processors to implement any of the hydraulic support reliability optimization methods provided in the embodiments of the present invention.

[0030] The hydraulic support reliability optimization method, apparatus, electronic device, and storage medium provided in the embodiments of the present invention can construct a radial basis function surrogate model based on an acquired initial sample set of the hydraulic support. The radial basis function surrogate model consists of k radial basis functions, where k is less than the initial sample number N. Each radial basis function corresponds to a center point and a width parameter. The radial basis function surrogate model is constructed by optimizing the center point and the width parameter using a fungal growth optimization algorithm, and the reliability of the hydraulic support is optimized based on the radial basis function surrogate model. Since the number of center points k in the radial basis function surrogate model is less than the initial sample number N, the model complexity is reduced, thereby reducing the computational resource consumption required for model training and prediction. Simultaneously, the global optimization of the center point and width parameter using the fungal growth optimization algorithm reduces the number of calls to finite element simulation and improves prediction accuracy. Therefore, it can reduce computational costs and improve reliability optimization efficiency. Attached Figure Description

[0031] 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, 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.

[0032] Figure 1 A flowchart illustrating a reliability optimization method for a hydraulic support provided in an embodiment of the present invention;

[0033] Figure 2 The cross-sectional shape of the top beam of the hydraulic support adopts a symmetrical three-chamber box structure.

[0034] Figure 3 A schematic diagram of radial basis function surrogate model parameter optimization provided for embodiments of the present invention;

[0035] Figure 4 A schematic diagram of the model accuracy of the radial basis function surrogate model provided for embodiments of the present invention;

[0036] Figure 5 Another flowchart of a reliability optimization method for a hydraulic support provided in an embodiment of the present invention;

[0037] Figure 6 A schematic diagram illustrating the change in reliability index of the optimized radial basis function surrogate model provided for embodiments of the present invention;

[0038] Figure 7 A schematic diagram illustrating the change in the objective function value during the optimization process, provided for an embodiment of the present invention;

[0039] Figure 8 This is a schematic diagram of a single-degree-of-freedom system.

[0040] Figure 9 for Figure 8 A schematic diagram illustrating the iteration of the corresponding reliability index;

[0041] Figure 10 A detailed flowchart of a reliability optimization method for hydraulic supports provided in an embodiment of the present invention;

[0042] Figure 11 A schematic diagram of a reliability optimization device for a hydraulic support provided in an embodiment of the present invention;

[0043] Figure 12 A schematic diagram of an electronic device provided as an embodiment of the present invention. Detailed Implementation

[0044] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0045] It should be understood that the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0046] In a first aspect, embodiments of the present invention provide a reliability optimization method for hydraulic supports, which can reduce computational costs and improve reliability optimization efficiency.

[0047] like Figure 1 As shown, an embodiment of the present invention provides a method for optimizing the reliability of a hydraulic support, the method including:

[0048] S11, Obtain the initial sample set of the hydraulic support. The initial sample set contains at least N samples. Each sample includes the design parameters of the first force-bearing component of the hydraulic support, as well as the target response value and limit response value corresponding to the design parameters. N is a positive integer, and the design parameters are d-dimensional vectors, where d is a positive integer.

[0049] In this step, an initial sample set of the first load-bearing component of the hydraulic support can be obtained. Reliability optimization of the hydraulic support refers to finding the optimal design parameters that ensure the structure of the first load-bearing component meets performance requirements and reliability constraints, while considering uncertainties such as manufacturing errors and load randomness. The vector formed by the design parameters can be a d-dimensional vector combining multiple geometrical parameters of the first load-bearing component of the hydraulic support, where each dimension represents an adjustable parameter. For example, design parameters such as the thickness of the upper cover plate of the first load-bearing component of the hydraulic support can be combined into a 7-dimensional vector. The target response value can be used to characterize the performance indicators of the first load-bearing component of the hydraulic support, such as structural mass. The limit response value is used to characterize the response of the first load-bearing component of the hydraulic support under extreme conditions, such as the maximum stress it withstands under extreme working conditions.

[0050] S12, Based on the initial sample set, a radial basis function surrogate model is constructed, wherein the radial basis function surrogate model consists of k radial basis functions, each of which corresponds to a center point and a width parameter. The center point and the width parameter are optimized using a fungal growth optimization algorithm, and the radial basis function surrogate model is constructed based on the optimized center point and the width parameter, wherein k is less than N;

[0051] In this step, a radial basis function (RBF) surrogate model is constructed based on the initial sample set. The RBF surrogate model is a mathematical model that approximates the true input-output mapping through a weighted combination of several radial basis functions; its accuracy is highly dependent on the center point position and width parameter of each basis function. In this embodiment of the invention, a fungal growth optimization algorithm (FGO) is used to globally optimize the center point and width parameters. For example, multiple center points and width parameters can be encoded as mycelia, and with the goal of minimizing fitness, iterative evolutionary behavior such as mycelial tip growth, lateral branching, and spore germination is simulated to globally optimize the center point and width parameters.

[0052] S13, Based on the radial basis function surrogate model, the reliability of the hydraulic support is optimized.

[0053] In this step, the reliability of the hydraulic support can be optimized. Specifically, based on the completed radial basis function surrogate model, the design parameters that can meet the structural performance requirements and reliability constraints of the first load-bearing component of the hydraulic support under different design parameter vectors are evaluated by calling the surrogate model. Based on this, and considering the random fluctuations of design parameters (such as machining tolerances), the design scheme that meets the preset reliability requirements and optimizes the target performance is found through multiple iterations.

[0054] The reliability optimization method for hydraulic supports provided in this invention can construct a radial basis function surrogate model based on an initial sample set of the hydraulic support. This surrogate model consists of k radial basis functions, where k is less than the initial sample size N. Each radial basis function corresponds to a center point and a width parameter. The surrogate model is constructed by optimizing the center point and width parameter using a fungal growth optimization algorithm. The reliability of the hydraulic support is then optimized based on this surrogate model. Since the number of center points k in the surrogate model is less than the initial sample size N, the model complexity is reduced, thereby reducing the computational resources required for model training and prediction. Simultaneously, the global optimization of the center point and width parameter using the fungal growth optimization algorithm reduces the number of calls to finite element simulation and improves prediction accuracy. Therefore, it can reduce computational costs and improve reliability optimization efficiency.

[0055] Specifically, in this embodiment of the invention, the first load-bearing component may include a top beam or a base. For example, in one embodiment, the first load-bearing component is a symmetrical three-chamber box-shaped structure, and the design parameters include the thickness of the top cover plate, the thickness of the bottom plate, the thickness of the stiffening ribs, the thickness of the side plates, the half-spacing of the stiffening ribs, the width of the box, and the thickness of the box.

[0056] Figure 2 The diagram shows the symmetrical three-chamber box-type cross-section of the top beam of a gantry hydraulic support. The primary load-bearing components of the hydraulic support, such as the top beam and base, are all multi-chamber box-type structures welded from steel plates. The top beam directly contacts the tunnel roof, bearing the roof pressure, while the base bears the reaction force from the floor and transmits the load. (See diagram.) The thickness of the top cover plate. For the thickness of the base plate, For the thickness of the stiffening plate, The thickness of the left and right side panels. This is the half-spacing of the stiffeners, i.e., the spacing relative to the center of symmetry of the cross-section. The width of the top beam box body. The thickness of the top beam box girder. These structural parameters directly affect the quality, reliability, and stress distribution of the top beam; therefore, these box girder section parameters are selected as design variables for reliability optimization design. According to the "Technical Conditions for Manufacturing Hydraulic Support Structural Components MT / T 587-2011", the ranges and deviations of each design parameter are shown in Table 1.

[0057]

[0058] Specifically, in step S11, the initial sample set of the hydraulic support can be obtained by combining the structural parameters, working conditions, and other core influencing factors of the hydraulic support, and selecting a reasonable sampling method to generate design samples and establish the initial sample set. For example, in one embodiment, obtaining the initial sample set of the hydraulic support may include: generating the initial design samples of the hydraulic support using Latin hypercube sampling; performing finite element simulation of the hydraulic support on each set of samples to obtain the mass response value and maximum stress response value of the first stress-bearing component corresponding to each set of samples, and constructing the initial sample set.

[0059] by Figure 2 For the hydraulic support example, the Latin hypercube sampling (LHS) method was used to generate initial sample points in the design variable space to determine the homogeneity and representativeness of the samples in the multidimensional space. Finite element simulation was performed on each sample point to extract the corresponding structural mass and maximum stress value, which were used as the numerical responses of the objective function and limit state function, respectively. The initial sample set is shown in Table 2.

[0060]

[0061] After obtaining the initial sample set of the hydraulic support in S11, a radial basis function surrogate model can be constructed based on the initial sample set. For example, in one embodiment, constructing the radial basis function surrogate model based on the initial sample set may include: encoding the k center points and k width parameters as mycelia based on the initial sample set; using the root mean square error between the predicted value of the objective function sub-model and the true value in the initial sample set, and the root mean square error between the predicted value of the limiting state sub-model and the true value in the initial sample set, respectively, as fitness indices, obtaining preferred mycelia through regional differential growth iteration of a fungal growth optimization algorithm, and determining preferred center points and preferred width parameters, wherein the regional differentiation includes eutrophic regions or hypotrophic regions, the fitness index corresponding to the eutrophic region is less than a preset threshold, and the fitness value corresponding to the hypotrophic region is greater than or equal to the preset threshold; and determining a preferred radial basis function surrogate model based on the preferred center points and the preferred width parameters.

[0062] As a further refinement of the above scheme, the internal structure of the radial basis function surrogate model can be further defined. For example, in one embodiment, the radial basis function surrogate model may include an objective function sub-model and a limit state sub-model, wherein the objective function sub-model is used to determine the mapping relationship between the design parameters and the mass of the first load-bearing component of the hydraulic support, and the limit state sub-model is used to determine the mapping relationship between the design parameters and the maximum stress of the first load-bearing component of the hydraulic support.

[0063] Specifically, the objective function sub-model focuses on establishing a nonlinear mapping between design parameters (such as plate thickness and stiffener spacing) and the mass of the top beam structure, while the limit state sub-model focuses on the mapping between design parameters and maximum stress. In the reliability optimization of hydraulic supports, mass needs to be minimized, and stress needs to meet allowable stress constraints; these two have different physical meanings and response characteristics. Through a clearly defined sub-model structure, the mutual interference that may occur when a single model simultaneously fits multiple objectives is avoided, thereby improving the reliability and prediction accuracy of the surrogate model in its respective prediction task.

[0064] As a supplement to the above scheme, the selection rules for the number of basis functions k in the radial basis function surrogate model can be limited. For example, in one embodiment, the number of radial basis functions k is determined according to the dimension d of the design parameter.

[0065] In practice, the number of radial basis functions (RBF) k is not a fixed value, but is dynamically determined based on the dimension d of the design parameters. A commonly used rule of thumb is the "10d rule," i.e., k = 10 × d. For example, in the optimization example of the top beam of a portal hydraulic support, the design parameters d = 7 (thickness of the top cover plate, bottom plate, stiffener plate, side plate, stiffener plate half-spacing, box width, and box thickness), then k = 10 × 7 = 70. This ensures that the number of RBF functions matches the complexity of the problem: the larger d is, the more basis functions are needed to capture high-dimensional nonlinearity; the smaller d is, the fewer basis functions are needed to avoid overfitting. In addition, k can also take values ​​between 5d and 15d, which can be flexibly configured according to the initial number of samples N and computational resources. Since k is much smaller than the total number of samples N in the conventional RBF method, this implementation reduces the model complexity without causing overfitting due to too many parameters, thereby improving the versatility of the method.

[0066] Building upon this, in order to apply the Fungal Growth Optimization Algorithm (FGO) to parameter optimization of the Radial Basis Function (RBF) model, this embodiment specifically designs the encoding method for mycelia in the algorithm. For example, in one implementation, each mycelia in the Fungal Growth Optimization Algorithm is encoded as a vector with dimensions k×d+k, where each mycelia contains k center points and width parameters corresponding to the radial basis functions, each center point is a d-dimensional vector, and each width parameter is a scalar.

[0067] Specifically, the mycelium is the fundamental solution unit in the fungal growth optimization algorithm, used to characterize a set of candidate radial basis function hyperparameters. The vector has a dimension of k×d+k, and its structure is as follows: the first k×d components correspond to k center points, each center point being a d-dimensional vector (d being the dimension of the design parameters); the last k components correspond to k width parameters, each width parameter being a scalar. For example, assuming the design parameter dimension d=7 (such as the thickness of the top cover plate, the thickness of the bottom plate, etc., 7 parameters), and the number of radial basis functions k=10, then the length of each mycelium vector is 10×7+10=80. The first 70 components represent 10 center points (each center point containing 7 coordinate values), and the last 10 components represent 10 width parameters. This encoding method encapsulates the center points and width parameters uniformly, facilitating crossover, mutation, and other operations in subsequent iterative evolution.

[0068] This embodiment encodes the center point and width parameters into a unified mycelial vector, enabling the fungal growth optimization algorithm to simultaneously optimize both types of hyperparameters. For high-dimensional design parameter scenarios, this embodiment uses integrated encoding to maintain the matching relationship between the center point and width parameters, thereby improving the prediction accuracy of the surrogate model.

[0069] The following uses the initial samples shown in Table 2 to illustrate the construction process of the radial basis function surrogate model.

[0070] Specifically, the objective function response value for each initial sample point can be calculated separately. and the limit state function response value An initial sample set is constructed based on the corresponding response values ​​calculated from the selected initial sample points. Sub-models of the objective function are then constructed based on the initial sample set. and limit state function sub-model The process of building an agent model is as follows: Figure 3 As shown, the specific steps are as follows:

[0071] (1) Generate M initial solutions Each mycelium Represent a group .

[0072] (2) For each mycelium The fitness index is calculated using the root mean square error of the objective function sub-model and the limit state sub-model corresponding to Equation (1), respectively, to evaluate the fitness. The smaller the fitness, the higher the prediction accuracy of the surrogate model under this set of hyperparameters.

[0073] (1)

[0074] (3) Based on the relationship between fitness value and preset threshold, determine the nutrient region of each mycelium: if the fitness is less than the threshold, it is in a nutrient-rich region; otherwise, it is in a nutrient-poor region. Behavioral discrimination is performed on each mycelium, and three mycelial behaviors are randomly selected: tip growth, lateral branching, and spore germination. The growth behavior of the mycelium replicates its extension and chemotaxis to precisely explore and find space, thereby reaching and developing nutrient-rich areas. For a given population size N, each mycelium... First, determine whether the location is nutrient-rich based on the fitness value, defining equations (2) and (3):

[0075] (2)

[0076] In the formula Indicates the first The fitness value of each solution. It is a relatively small number, if Less than the following formula defined If so, it indicates that the area is in a eutrophic zone.

[0077] (3)

[0078] In the formula The predetermined probability between [0,1] determines the trade-off between the exploration and development strategies. For the current subalgebra, This represents the maximum number of offspring.

[0079] For mycelia in eutrophic areas, we will attempt to explore new areas to achieve better nutrition by randomly selecting two individuals from the population. The difference between them is calculated as the growth direction, and an exponential function related to the current fitness value is introduced to simulate the growth rate, as shown in equation (4):

[0080] (4)

[0081] In the formula Given a random number in the interval [0,1], the newly grown mycelium can be calculated using equation (5):

[0082] (5)

[0083] In the formula For a random value of the j-th dimension generated between [0,1], A random number within the range [0,1] For the dimension of the solution, Indicates Iverson brackets, if If it is false, then Convert to 0, otherwise convert to 1.

[0084] For mycelia in low-nutrient areas, we will try to apply development strategies to move them to nutrient-rich areas. To simulate chemotaxis, we will divide them into two states. The first state is to grow in the direction of the mycelia with the highest current fitness value with a certain probability, i.e., Equation (6):

[0085] (6)

[0086] In the formula All numbers are random numbers within the interval [0,1]. A vector of random numbers in the interval [0,1]. It is a predefined parameter between [0,1]. Randomly select -1 or 1. If the current individual is optimal, then the newly grown mycelium can be obtained using equation (7):

[0087] (7)

[0088] In the formula A random number between [0,1] The growth rate is defined by equation (8). To explore the step size, it is defined by equation (9):

[0089] (8)

[0090] In the formula It is a random number between [0,1].

[0091] (9)

[0092] In the formula It is a random number between [0,1].

[0093] The second state is due to reverse growth caused by the presence of a certain harmful chemical substance, namely, equation (10):

[0094] (10)

[0095] In the formula If the number is a random number between [0,1], then the newly grown mycelium can be obtained by equation (11):

[0096] (11)

[0097] In the formula It is a random number in the interval [0,1].

[0098] This behavior provides FGO with multiple search modes, improving FGO's performance and preventing it from getting stuck in local optima, thus reducing its slow convergence speed.

[0099] Branching behavior replicates how new hyphal branches generated from one side of existing hyphae explore the surrounding area to find more nutrients. The growth rate of lateral branches can be expressed by equation (12):

[0100] (12)

[0101] In the formula It is a random number between [0,1].

[0102] The newly branched mycelium can be obtained by equation (13):

[0103] (13)

[0104] Spore germination behavior represents how existing hyphae explore new environments to reach safer and more nutrient-rich areas. When spores land in an environment rich in moisture and nutrients, they germinate and grow. The new hyphae that exhibit this behavior are defined by equation (14):

[0105] (14)

[0106] In the formula Randomly select -1 or 1.

[0107] These two behaviors enable the algorithm to escape local optima, increasing population diversity and global exploration capabilities.

[0108] (4) Calculate the number of new mycelia produced by each mycelium based on its behavior. .

[0109] (5) Calculate the number of new mycelia. The fitness value, and its relationship with each The process involves comparison, with individuals exhibiting higher fitness carried over to the next generation until the maximum number of generations is reached, at which point the iteration stops. This allows the selection of the mycelium with the lowest fitness from the final population as the preferred mycelium, whose center point and width parameters are the preferred hyperparameters. In other words, the solution represented by the mycelium with the highest fitness value in the population is the optimal solution. At this point, It can be calculated analytically using the least squares method:

[0110]

[0111] (15)

[0112] In the formula for The pseudo-inverse of the model can be predicted as:

[0113] (16)

[0114] This invention introduces a regionally differentiated growth strategy, enabling mycelia at different fitness levels to adopt different search behaviors. By combining the fine development of eutrophic regions with the extensive exploration of nutrient-poor regions, the global optimal parameters can be effectively discovered, thereby improving the generalization ability of the surrogate model.

[0115] After obtaining the preferred surrogate model in S11, before reliability optimization, in order to further improve the prediction accuracy of the model near the limit state surface, this embodiment introduces an adaptive point addition strategy. For example, in one embodiment, after determining the preferred radial basis function surrogate model based on the preferred center point and the width parameter, and before optimizing the reliability of the hydraulic support based on the radial basis function surrogate model, the method may further include: based on the radial basis function surrogate model, with the goal of improving the prediction accuracy of the model near the limit state surface, and in combination with dynamic distance constraints, searching for new sample points within a preset distance range from the limit state surface, wherein the limit state surface is a continuous surface composed of the design parameter vectors whose predicted values ​​of the limit state sub-model are equal to zero; performing finite element simulation on the new sample points to obtain the corresponding target response value and limit response value, adding the new sample point and its corresponding target response value and limit response value as a new sample to the sample set; retraining the radial basis function surrogate model based on the updated sample set to obtain a corresponding preferred radial basis function surrogate model, and then jumping back to the step of searching for new sample points near the limit state surface based on the radial basis function surrogate model with the goal of improving the prediction accuracy of the model near the limit state surface and in combination with dynamic distance constraints, continuing to execute the iteration until the model accuracy meets the preset stopping criterion, and obtaining the updated preferred radial basis function surrogate model.

[0116] Specifically, based on the currently preferred radial basis function surrogate model, the continuous surface formed by the set of points whose predicted values ​​of the limit state sub-model are equal to zero is defined as the limit state surface. New sample points are searched for near this surface through optimization search—the search objective is to maximize the prediction uncertainty or prediction error of the surrogate model at the limit state surface, while being constrained by dynamic distance to avoid the new samples being too close to existing samples. The coordinates of the new sample points obtained from the search are passed to the finite element simulation module for simulation calculation, outputting the true mass response value and the maximum stress response value of the point. These two true response values, along with the design parameter vector of the new sample point, are added to the sample set as a new sample. The updated sample set is sent back to the surrogate model training module to re-execute the training process, including mycelial encoding, FGO optimization, and least squares solving, to obtain the updated preferred surrogate model. The above process is iterated cyclically, with data flowing in a closed loop of "surrogate model → limit state surface → new sample point → finite element simulation → sample set → surrogate model" in each iteration until the model accuracy converges.

[0117] The mathematical expression for this embodiment can be represented as follows:

[0118] (17)

[0119] in, It is the first The new sample points found in the next iteration using the point addition strategy For added A sample set of 1 sample point.

[0120] By solving the above equations, new sample points can be found. In practice, reliability constraints can be temporarily omitted, and the optimization objective can be solely to improve model accuracy. At the same time, the randomness of design variables and related parameters can be ignored, and each random variable and random parameter can be fixed at its mean point for analysis, which is equivalent to a deterministic optimization problem.

[0121] During the optimization iteration process, to avoid the algorithm getting stuck in a local optimum, dynamic distance constraints can be imposed. For example, in one implementation, the threshold of the dynamic distance constraint is used to control the minimum distance between new sample points and existing sample points. Specifically, to prevent new sample points from excessively clustering in local areas, a dynamic distance constraint strategy is used to regulate the distribution density of sample points, thereby improving the global approximation accuracy of the surrogate model in the limit state surface region. The value of the dynamic distance constraint can be calculated by equation (18):

[0122] (18)

[0123] After solving for the new sample points, for the new sample points Perform simulation to obtain the objective function response value and limit state function response value Then, add it to the sample set to update the sample set. Rebuild the proxy model based on the updated sample set.

[0124] In practical implementation, to achieve a balance between model accuracy and computational efficiency, this embodiment provides a stopping criterion for the adaptive point addition process. For example, in one implementation, the preset stopping criterion is that the average rate of change of the determination coefficients of the limit state sub-model is less than a preset threshold in three consecutive iterations.

[0125] In the adaptive addition of sample points, the main performance indicators RMSE and R² are selected as the criteria for judging the model accuracy, with a greater focus on the accuracy of the limit state function surrogate model. Therefore, the stopping criterion for this step is set as follows: when the average rate of change of R² for three consecutive times is less than a threshold (e.g., 0.005), the addition of sample points is stopped. The mathematical expression is:

[0126] (19)

[0127] Understandably, when the surrogate model's accuracy is sufficiently high, adding new samples has limited impact on improving model performance and may even increase the computational cost of finite element simulation. Therefore, by monitoring the stabilization trend of R², an optimal balance between accuracy and efficiency can be achieved.

[0128] The changes in RMSE and R² of the objective function sub-model and the limit state sub-model of the addition process are as follows: Figure 4 As shown. (Through) Figure 4 It can be seen that as the number of sample points increases, the accuracy of both the standard function sub-model and the limit state sub-model gradually increases. Although at the beginning of adding points, due to the small number of sample points, the newly added sample points have a significant impact on RMSE and R2, resulting in large fluctuations, the overall trend is that RMSE is lower and R2 is higher. Moreover, as the number of sample points increases, the fluctuations gradually weaken. When 28 new sample points are added, the performance of the limit state function improves relatively slowly with the addition of sample points. When 34 sample points are added, the accuracy meets the stopping condition. Considering the balance between accuracy and efficiency, no more points are added.

[0129] After constructing the radial basis function surrogate model based on the initial sample set in step S12, the reliability of the hydraulic support can be optimized based on the radial basis function surrogate model. For example, such as... Figure 5 As shown, in one embodiment, the reliability optimization of the hydraulic support based on the radial basis function surrogate model may include:

[0130] S21, the design parameters of the hydraulic support are converted to the standard normal space, the estimated value of the most likely failure point is initialized to the mean point of the design parameters, and the constraint offset is initialized to zero. The most likely failure point is the point that satisfies the condition that the prediction value of the limit state sub-model is zero and the probability density is the largest.

[0131] In this step, you can set the initial offset. The initial most likely point is 0. for , for .

[0132] S22, with the goal of minimizing the quality predicted by the objective function sub-model, and with the constraint that the stress margin predicted by the limit state sub-model plus the constraint offset is greater than or equal to zero, the radial basis function surrogate model is deterministically optimized to obtain candidate design points;

[0133] In this step, the optimal solution in the current iteration can be found using a genetic algorithm.

[0134] S23, For the candidate design point, according to the preset random distribution of the design parameters, multiple sample points are generated by Monte Carlo simulation, the limit state function value of each sample is predicted by the limit state sub-model, the proportion of samples with limit state function values ​​less than zero is counted as the failure probability, and the reliability of the candidate design point is determined.

[0135] In this step, a large number of Monte Carlo simulation sample points are generated at the current optimal solution, and the limit state function response values ​​of each point are obtained by using the surrogate model. The reliability under the current design is estimated by using Equation (20).

[0136] (20)

[0137] S24. If the reliability of the candidate design point does not meet the preset target reliability, the most likely failure point corresponding to the candidate design point is determined in the standard normal space, and the constraint offset is updated according to the difference between the target reliability index and the reliability index corresponding to the current most likely failure point.

[0138] In this step, the design variables can be transformed into a standard normal distribution space to solve for the point where failure is most likely under the current optimal design. Based on this, and combined with the target reliability index, the constraint offset for the next iteration can be calculated. .

[0139] S25, add the most likely failure point to the sample set, update the sample set and retrain the radial basis function surrogate model, jump to step S22 to continue execution, iterate until the rate of change of the objective function value obtained by consecutive M deterministic optimizations is less than a preset threshold, and the reliability of the candidate design point meets the preset reliability, output the candidate design point as the final optimization result, where the value of M ranges from 2 to 6.

[0140] In this step, the objective function response value and the limit state function response value can be obtained by simulating the new sample points, and then added to the sample set to update the sample set. The surrogate model is then reconstructed based on the updated sample set. Specifically, in this process, the reliability gradually approaches the target reliability with each iteration. Therefore, the stopping criterion is set as follows: iteration stops when the average rate of change of the objective function is less than 1 for three consecutive iterations, and the target reliability is met. The optimal solution at this point is the optimal design, mathematically expressed as:

[0141] (twenty one)

[0142] In this implementation, reliability optimization employs a strategy combining sequential optimization and Monte Carlo simulation. The specific iterative process can be expressed mathematically as follows:

[0143] (twenty two)

[0144] in, It is the offset, representing the displacement required from the current design level towards the target reliability design level. These are the design variables transformed into the standard normal distribution design space. It is a target reliability indicator. This is the point where failure is most likely to occur under the current design.

[0145] Figure 6 shows the reliability index variation curves during sequence optimization and Monte Carlo simulation (MCS) based on a target reliability index of 2.7174. From... Figure 6 It can be seen that the reliability of the top beam is relatively low at the beginning of the sequential reliability optimization. However, as the sequential reliability optimization proceeds, the reliability gradually increases and approaches the target reliability after 26 iterations, showing a convergence trend with small fluctuations.

[0146] The change in the objective function value throughout the optimization process is as follows: Figure 7 As shown. By Figure 7As can be seen, in the sequential reliability optimization process, after 32 iterations, the objective function value shows a convergence trend, and after 36 iterations, the stopping condition is reached. At the same time, the reliability of the top beam meets the target reliability requirement. The optimal solution at this time is the optimal set of structural parameters. The optimal structural solution and its corresponding parameters obtained by the adaptive sequential reliability optimization method based on the radial basis function surrogate model are shown in Table 3.

[0147]

[0148] Taking all factors into consideration Figure 6 , Figure 7 As shown in Table 3, the optimization results meet the preset reliability constraints, all design variables are within the feasible range, and the structure still maintains a reliable working state under the influence of uncertain factors (including load disturbance and processing error). This indicates that the adaptive sequential reliability optimization method based on the radial basis function surrogate model also shows stable convergence and effectiveness in the actual engineering problem of the portal hydraulic support top beam structure, and has good adaptability in dealing with complex design space and random disturbance.

[0149] The following is a specific verification process given in the embodiments of the present invention.

[0150] To comprehensively evaluate the predictive performance of the proposed radial basis function surrogate model FGO-RBF, a practical example of a non-linear oscillator problem with an engineering background was used. Five performance indicators were selected for comprehensive analysis: root mean square error (RMSE), coefficient of determination (R2), mean absolute error (MAE), mean bias error (MBE), and maximum error (Max Error). The performance of each indicator was compared with that of various other models, including the conventional RBF model, the Kriging model, the PSO-RBF model, and the MLP model.

[0151] The non-linear Oscillator problem is a nonlinear, undamped, single-degree-of-freedom vibration system with six random variables, whose mathematical function is shown in equation (23):

[0152] (twenty three)

[0153] in The frequency of this single-degree-of-freedom vibration system is:

[0154] Figure 8 The schematic diagram of the single-degree-of-freedom system shown is illustrated in Table 4, and its random design variable information is also shown in Table 4.

[0155]

[0156] The performance metrics of each model are shown in Table 5:

[0157]

[0158] As can be seen from the table, in this nonlinear undamped single-degree-of-freedom vibration system, the radial basis function surrogate model FGO-RBF performs slightly worse than a certain PSO-RBF model in terms of MBE index, but it is still significantly better than other models in other major performance indices, which shows its modeling ability and generalization performance in complex practical problems.

[0159] The proposed adaptive sequential reliability optimization method based on the FGO-RBF model is compared and analyzed with current mainstream reliability optimization methods using a typical reliability optimization problem.

[0160] A widely applied reliability optimization problem is expressed as:

[0161] (twenty four)

[0162] in Follows a normal distribution , and These are the design variables for the intervals [0, 3.7] and [0, 4], respectively. The specified target reliability index... The value is 2. The specific constraint function is:

[0163] (25)

[0164] The initial number of sample points was set to 10, and optimization was carried out gradually. Figure 9 The figure shows the iterative process of the reliability index of the constraint function. As can be seen from the figure, the reliability index fluctuates greatly in the first four iterations because the offset is large. As the iteration progresses, it gradually approaches the target reliability and the offset gradually decreases. After 12 iterations, the reliability index meets the convergence condition. During this process, constraint function 1 converges to the target reliability index 2.0, while constraint function 2 remains at a high reliability index.

[0165]

[0166] Table 6 shows the optimization results using different reliability optimization methods, including the objective function value of the optimal point, the reliability index of the constraints, and the number of function calls. It can be seen that PMA, SORA, HAK-SLA, Quantile-based RBDO, and the method in this paper can all successfully converge to their respective optimal solutions. Among them, SORA and PMA methods have the most function calls, far exceeding HAK-SLA and RBDO. The method in this paper has the fewest function calls, converging to the target reliability using only 10 initial samples and 28 additional samples. Although the objective function value is slightly larger than that of PMA, SORA, and HAK-SLA, these methods do not strictly satisfy the reliability constraints.

[0167] The following detailed description of the reliability optimization method for hydraulic supports provided by the embodiments of the present invention will be provided through specific examples.

[0168] like Figure 10 As shown, the reliability optimization method for hydraulic supports provided in the embodiments of the present invention may include:

[0169] S501. Initial design samples of hydraulic supports are generated using Latin hypercube sampling.

[0170] Optionally, the first load-bearing component of the hydraulic support includes a top beam or a base;

[0171] Optionally, the first load-bearing component is a symmetrical three-chamber box-type structure, and the design parameters include the thickness of the top cover plate, the thickness of the bottom plate, the thickness of the stiffening rib, the thickness of the side plate, the half-spacing of the stiffening rib, the width of the box, and the thickness of the box.

[0172] S502. Perform finite element simulation of the hydraulic support for each group of samples, obtain the mass response value and maximum stress response value of the first stressed component corresponding to each group of samples, and construct an initial sample set.

[0173] S503. Based on the initial sample set, encode the k center points and k width parameters into mycelia;

[0174] Optionally, the number of radial basis functions k is determined according to the dimension d of the design parameters;

[0175] Optionally, each mycelium in the fungal growth optimization algorithm is encoded as a vector with dimensions k×d+k, where each mycelium contains the center point and width parameter corresponding to k radial basis functions, each center point is a d-dimensional vector, and each width parameter is a scalar;

[0176] S504. Using the root mean square error between the predicted value of the objective function sub-model and the true value in the initial sample set, and the root mean square error between the predicted value of the limit state sub-model and the true value in the initial sample set, respectively, as fitness indicators, the optimal mycelium is obtained through the regional differential growth iteration of the fungal growth optimization algorithm, and the optimal center point and optimal width parameters are determined.

[0177] The regional differentiation includes eutrophic regions or hypotrophic regions, wherein the fitness index corresponding to the eutrophic region is less than a preset threshold, and the fitness value corresponding to the hypotrophic region is greater than or equal to the preset threshold.

[0178] S505. Based on the preferred center point and the preferred width parameter, determine the preferred radial basis function surrogate model;

[0179] Optionally, the radial basis function surrogate model includes an objective function sub-model and a limit state sub-model, wherein the objective function sub-model is used to determine the mapping relationship between the design parameters and the mass of the first load-bearing component of the hydraulic support, and the limit state sub-model is used to determine the mapping relationship between the design parameters and the maximum stress of the first load-bearing component of the hydraulic support;

[0180] S506. Based on the radial basis function surrogate model, with the goal of improving the prediction accuracy of the model near the limit state surface, and combined with dynamic distance constraints, new sample points are searched near the limit state surface, wherein the limit state surface is a continuous surface composed of the design parameter vectors whose predicted values ​​of the limit state sub-model are equal to zero.

[0181] Optionally, the threshold of the dynamic distance constraint is used to control the minimum distance between new sample points and existing sample points;

[0182] S507. Perform finite element simulation on the new sample point to obtain the corresponding target response value and limit response value, and add the new sample point and its corresponding target response value and limit response value as a new sample to the sample set.

[0183] S508. Retrain the radial basis function surrogate model based on the updated sample set to obtain a corresponding preferred radial basis function surrogate model. Then, jump to step S506 and continue to execute the iteration until the model accuracy meets the preset stopping criterion to obtain the updated preferred radial basis function surrogate model.

[0184] Optionally, the preset stopping criterion is that the average rate of change of the determination coefficient of the limit state sub-model is less than a preset threshold in three consecutive iterations;

[0185] S509. Based on the radial basis function surrogate model, the reliability of the hydraulic support is optimized.

[0186] Secondly, embodiments of the present invention provide a reliability optimization device for hydraulic supports, which can reduce computational costs and improve reliability optimization efficiency.

[0187] like Figure 11 As shown, embodiments of the present invention also provide a reliability optimization device for hydraulic supports, which may include:

[0188] The acquisition unit 31 is used to acquire an initial sample set of the hydraulic support. The initial sample set contains at least N samples. Each sample includes the design parameters of the first force-bearing component of the hydraulic support, as well as the target response value and limit response value corresponding to the design parameters. N is a positive integer, and the design parameters are d-dimensional vectors, where d is a positive integer.

[0189] Construction unit 32 is used to construct a radial basis function surrogate model based on the initial sample set, wherein the radial basis function surrogate model consists of k radial basis functions, each of which corresponds to a center point and a width parameter. The center point and the width parameter are optimized by a fungal growth optimization algorithm, and the radial basis function surrogate model is constructed based on the optimized center point and the width parameter, wherein k is less than N;

[0190] The optimization unit 33 is used to optimize the reliability of the hydraulic support based on the radial basis function surrogate model.

[0191] The reliability optimization device for hydraulic supports provided in this invention can construct a radial basis function surrogate model based on an acquired initial sample set of the hydraulic support. The surrogate model consists of k radial basis functions, where k is less than the initial sample number N. Each radial basis function corresponds to a center point and a width parameter. The surrogate model is constructed by optimizing the center point and width parameter using a fungal growth optimization algorithm, and the reliability of the hydraulic support is optimized based on this surrogate model. Since the number of center points k in the surrogate model is less than the initial sample number N, the model complexity is reduced, thereby reducing the computational resources required for model training and prediction. Simultaneously, the global optimization of the center point and width parameter using the fungal growth optimization algorithm reduces the number of calls to finite element simulation and improves prediction accuracy. Therefore, it can reduce computational costs and improve reliability optimization efficiency.

[0192] In one embodiment, the radial basis function surrogate model includes an objective function sub-model and a limit state sub-model, wherein the objective function sub-model is used to determine the mapping relationship between the design parameters and the mass of the first load-bearing component of the hydraulic support, and the limit state sub-model is used to determine the mapping relationship between the design parameters and the maximum stress of the first load-bearing component of the hydraulic support.

[0193] In one embodiment, each mycelium in the fungal growth optimization algorithm is encoded as a vector with dimensions k×d+k, wherein each mycelium contains center points and width parameters corresponding to k radial basis functions, each center point is a d-dimensional vector, and each width parameter is a scalar.

[0194] In one implementation, the construction unit 32 is specifically used to: encode the k centroids and k width parameters into mycelia based on the initial sample set; using the root mean square error between the predicted value of the objective function sub-model and the true value in the initial sample set, and the root mean square error between the predicted value of the limiting state sub-model and the true value in the initial sample set, respectively, as fitness indices, obtain preferred mycelia through regional differential growth iteration of a fungal growth optimization algorithm, and determine preferred centroids and preferred width parameters, wherein the regional differentiation includes eutrophic regions or hypotrophic regions, the fitness index corresponding to the eutrophic region is less than a preset threshold, and the fitness value corresponding to the hypotrophic region is greater than or equal to the preset threshold; and determine a preferred radial basis function surrogate model based on the preferred centroids and preferred width parameters.

[0195] In one embodiment, the device further includes: a search unit, configured to, after the construction unit 32 determines the preferred radial basis function surrogate model and before the reliability optimization of the hydraulic support based on the radial basis function surrogate model, search for new sample points within a preset distance range from the limit state surface, with the goal of improving the prediction accuracy of the model near the limit state surface, combined with dynamic distance constraints, wherein the limit state surface is a continuous surface composed of the design parameter vectors whose predicted values ​​of the limit state sub-model are equal to zero; a simulation unit, configured to perform finite element simulation on the new sample points, obtain the corresponding target response value and limit response value, and add the new sample points and their corresponding target response value and limit response value as a new sample to the sample set; a training unit, configured to retrain the radial basis function surrogate model based on the updated sample set to obtain a corresponding preferred radial basis function surrogate model; and a triggering unit, configured to trigger the search unit to continue execution, iterating cyclically until the model accuracy meets a preset stopping criterion, thereby obtaining the updated preferred radial basis function surrogate model.

[0196] In one implementation, the threshold of the dynamic distance constraint is used to control the minimum distance between new sample points and existing sample points.

[0197] In one implementation, the preset stopping criterion is that the average rate of change of the determination coefficient of the limit state sub-model is less than a preset threshold in three consecutive iterations.

[0198] In one embodiment, the optimization unit 33 includes: a conversion module, configured to convert the design parameters of the hydraulic support to a standard normal space, initialize the estimated value of the most likely failure point as the mean point of the design parameters, and initialize the constraint offset to zero, wherein the most likely failure point is the point that satisfies the condition that the predicted value of the limit state sub-model is zero and has the highest probability density; a deterministic optimization module, configured to perform deterministic optimization on the radial basis function surrogate model with the objective of minimizing the quality predicted by the objective function sub-model and with the constraint that the stress margin predicted by the limit state sub-model plus the constraint offset is greater than or equal to zero, to obtain candidate design points; and a Monte Carlo module, configured to generate multiple sample points for the candidate design points through Monte Carlo simulation based on a preset random distribution of the design parameters, and predict the limit state function of each sample using the limit state sub-model. The reliability of the candidate design point is determined by the proportion of samples with a limit state function value less than zero as the failure probability. An update module is used to determine the most likely failure point corresponding to the candidate design point in the standard normal space if the reliability of the candidate design point does not meet the preset target reliability. The constraint offset is updated based on the difference between the target reliability index and the reliability index corresponding to the current most likely failure point. A retraining module adds the most likely failure point to the sample set, updates the sample set, and retrains the radial basis function surrogate model. This triggers the deterministic optimization module to continue execution, iterating until the rate of change of the objective function value obtained from M consecutive deterministic optimizations is less than a preset threshold, and the reliability of the candidate design point meets the preset reliability. The candidate design point is then output as the final optimization result, where M ranges from 2 to 6.

[0199] In one implementation, the number k of the radial basis functions is determined according to the dimension d of the design parameters.

[0200] In one embodiment, the acquisition unit 31 is specifically used to: generate initial design samples of the hydraulic support using Latin hypercube sampling; perform finite element simulation of the hydraulic support for each set of samples, obtain the mass response value and maximum stress response value of the first force-bearing component corresponding to each set of samples, and construct the initial sample set.

[0201] In one embodiment, the first load-bearing component of the hydraulic support includes a top beam or a base.

[0202] In one embodiment, the first load-bearing component is a symmetrical three-chamber box-shaped structure, and the design parameters include the thickness of the top cover plate, the thickness of the bottom plate, the thickness of the stiffening ribs, the thickness of the side plates, the half-spacing of the stiffening ribs, the width of the box, and the thickness of the box.

[0203] Thirdly, embodiments of the present invention also provide an electronic device that can reduce computing costs and improve reliability optimization efficiency.

[0204] like Figure 12 As shown, the electronic device provided in the embodiments of the present invention may include: a processor 71 and a memory 72, wherein the processor 71 and the memory 72 are electrically connected; the memory 72 is used to store executable program code; the processor 71 runs a program corresponding to the executable program code by reading the executable program code stored in the memory 72, so as to realize any of the hydraulic support reliability optimization methods provided in the foregoing embodiments.

[0205] The specific execution process of the above steps by the processor 71, as well as the steps further executed by the processor 71 by running executable program code, can be found in the description of the foregoing embodiments, and will not be repeated here.

[0206] Fourthly, embodiments of the present invention also provide a computer-readable storage medium storing one or more programs, which can be executed by one or more processors to implement any of the hydraulic support reliability optimization methods provided in the foregoing embodiments, thus achieving the corresponding technical effects. This has been described in detail above and will not be repeated here.

[0207] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, 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 a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0208] The various embodiments in this specification are described in a related manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0209] In particular, the device embodiment is basically similar to the method embodiment, so the description is relatively simple. For relevant details, please refer to the description of the method embodiment.

[0210] For ease of description, the above apparatus is described by dividing it into various functional units / modules. Of course, in implementing this invention, the functions of each unit / module can be implemented in one or more software and / or hardware.

[0211] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0212] 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 reliability of a hydraulic support, characterized in that, include: Obtain an initial sample set for the hydraulic support, the initial sample set containing at least N samples, each sample including the design parameters of the first force-bearing component of the hydraulic support, and the target response value and limit response value corresponding to the design parameters, where N is a positive integer, the design parameters are d-dimensional vectors, and d is a positive integer; Based on the initial sample set, a radial basis function surrogate model is constructed, wherein the radial basis function surrogate model consists of k radial basis functions, each of which corresponds to a center point and a width parameter. The center point and the width parameter are optimized using a fungal growth optimization algorithm, and the radial basis function surrogate model is constructed based on the optimized center point and the width parameter, wherein k is less than N; Based on the radial basis function surrogate model, the reliability of the hydraulic support is optimized.

2. The reliability optimization method for hydraulic supports according to claim 1, characterized in that, The radial basis function surrogate model includes an objective function sub-model and a limit state sub-model. The objective function sub-model is used to determine the mapping relationship between the design parameters and the mass of the first load-bearing component of the hydraulic support, and the limit state sub-model is used to determine the mapping relationship between the design parameters and the maximum stress of the first load-bearing component of the hydraulic support.

3. The reliability optimization method for hydraulic supports according to claim 2, characterized in that, In the fungal growth optimization algorithm, each mycelium is encoded as a vector with dimensions k×d+k. Each mycelium contains the center point and width parameter corresponding to k radial basis functions. Each center point is a d-dimensional vector, and each width parameter is a scalar.

4. The reliability optimization method for hydraulic supports according to claim 3, characterized in that, The construction of the radial basis function surrogate model based on the initial sample set includes: Based on the initial sample set, the k center points and k width parameters are encoded as mycelia; The root mean square error between the predicted value of the objective function sub-model and the true value in the initial sample set, and the root mean square error between the predicted value of the limit state sub-model and the true value in the initial sample set are used as fitness indices. Through regional differential growth iteration of the fungal growth optimization algorithm, preferred mycelia are obtained, and preferred center point and preferred width parameters are determined. The regional differentiation includes eutrophic regions or hypotrophic regions. The fitness index corresponding to the eutrophic region is less than a preset threshold, and the fitness value corresponding to the hypotrophic region is greater than or equal to the preset threshold. Based on the preferred center point and the preferred width parameter, a preferred radial basis function surrogate model is determined.

5. The reliability optimization method for hydraulic supports according to claim 4, characterized in that, After determining the preferred radial basis function surrogate model based on the preferred center point and the width parameter, and before performing reliability optimization on the hydraulic support based on the radial basis function surrogate model, the method further includes: Based on the radial basis function surrogate model, with the goal of improving the prediction accuracy of the model near the limit state surface, and combined with dynamic distance constraints, new sample points are searched within a preset distance range from the limit state surface, wherein the limit state surface is a continuous surface formed by the design parameter vectors whose predicted values ​​of the limit state sub-model are equal to zero. Perform finite element simulation on the new sample point to obtain the corresponding target response value and limit response value, and add the new sample point and its corresponding target response value and limit response value as a new sample to the sample set; The radial basis function surrogate model is retrained based on the updated sample set to obtain a corresponding preferred radial basis function surrogate model. The process then jumps to the step of improving the prediction accuracy of the model near the limit state surface based on the radial basis function surrogate model, combined with dynamic distance constraints, to search for new sample points within a preset distance range from the limit state surface. The step of searching for new sample points within a preset distance range from the limit state surface, where the limit state surface is a continuous surface formed by the design parameter vectors whose predicted values ​​of the limit state sub-model are equal to zero, continues to be executed. This process is iterated until the model accuracy meets the preset stopping criterion, resulting in the updated preferred radial basis function surrogate model.

6. The reliability optimization method for hydraulic supports according to claim 5, characterized in that, The threshold of the dynamic distance constraint is used to control the minimum distance between new sample points and existing sample points.

7. The method according to claim 5, characterized in that, The preset stopping criterion is that the average rate of change of the determination coefficient of the limit state sub-model is less than a preset threshold in three consecutive iterations.

8. The reliability optimization method for hydraulic supports according to claim 5, characterized in that, The reliability optimization of the hydraulic support based on the radial basis function surrogate model includes: The design parameters of the hydraulic support are transformed into a standard normal space. The estimated value of the most likely failure point is initialized to the mean point of the design parameters, and the constraint offset is initialized to zero. The most likely failure point is the point that satisfies the condition that the prediction value of the limit state sub-model is zero and the probability density is the largest. With the goal of minimizing the quality predicted by the objective function sub-model, and with the constraint that the stress margin predicted by the limit state sub-model plus the constraint offset is greater than or equal to zero, the radial basis function surrogate model is deterministically optimized to obtain candidate design points. For the candidate design points, multiple sample points are generated through Monte Carlo simulation based on the preset random distribution of the design parameters. The limit state function value of each sample is predicted using the limit state sub-model. The proportion of samples with limit state function values ​​less than zero is used as the failure probability to determine the reliability of the candidate design points. If the reliability of the candidate design point does not meet the preset target reliability, the most likely failure point corresponding to the candidate design point is determined in the standard normal space, and the constraint offset is updated according to the difference between the target reliability index and the reliability index corresponding to the current most likely failure point. The most likely failure point is added to the sample set. After updating the sample set, the radial basis function surrogate model is retrained. The process then jumps to the step of performing deterministic optimization on the radial basis function surrogate model with the objective of minimizing the quality predicted by the objective function sub-model and the constraint that the stress margin predicted by the limit state sub-model plus the constraint offset is greater than or equal to zero. This process continues until the rate of change of the objective function value obtained by M consecutive deterministic optimizations is less than a preset threshold, and the reliability of the candidate design point meets the preset reliability. The candidate design point is then output as the final optimization result, where the value of M ranges from 2 to 6.

9. The reliability optimization method for hydraulic supports according to claim 1, characterized in that, The number k of the radial basis functions is determined according to the dimension d of the design parameters.

10. The reliability optimization method for hydraulic supports according to claim 1, characterized in that, The process of obtaining the initial sample set for the hydraulic support includes: The initial design sample of the hydraulic support was generated using Latin hypercube sampling; For each set of samples, perform finite element simulation of the hydraulic support to obtain the mass response value and maximum stress response value of the first force-bearing component corresponding to each set of samples, and construct the initial sample set.

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