Method for calculating gravity dam deep sliding reliability based on optimized extreme learning machine

Abstract

The application discloses a gravity dam deep sliding reliability calculation method based on an optimized extreme learning machine, relates to the technical field of hydraulic structure engineering, and comprises the following steps: obtaining basic information of a gravity dam; optimizing an extreme learning machine by using a multi-strategy fusion improved particle swarm optimization algorithm SHPSO to construct an optimized extreme learning machine ELM model; constructing an optimal ELM model according to optimal parameters of the optimized extreme learning machine ELM model and calculating the gravity dam deep sliding reliability. The application lays a foundation for calculation by obtaining the basic information of the gravity dam; the ELM parameters are taken as the optimization target, the multi-strategy fusion improved particle swarm optimization algorithm SHPSO is used to optimize the ELM parameters, the prediction precision and the generalization ability of the ELM model are improved; the optimal model is constructed according to the optimal parameters of the optimized ELM model, random samples are input for calculation, the gravity dam deep sliding failure rate and the reliability can be accurately obtained, accurate data support is provided for dam body anti-sliding stability analysis, and the defects of the existing method are made up.

Description

Technical Field

[0001] This invention relates to the field of hydraulic structure engineering technology, and in particular to a method for calculating the deep sliding reliability of gravity dams based on optimized limit learning machine. Background Technology

[0002] In recent years, with the continuous expansion of engineering project scale and the increasing complexity of engineering conditions, gravity dam anti-sliding stability analysis has become a crucial step in the construction of major water conservancy and hydropower projects. Traditional methods for analyzing gravity dam anti-sliding stability are mostly based on empirical formulas or simplified assumptions, making it difficult to accurately reflect actual engineering conditions and thus failing to meet the needs of modern engineering design. To address this issue, scholars have recently begun applying machine learning algorithms to analyze and predict the anti-sliding stability of dams.

[0003] While existing machine learning-based methods for analyzing the anti-sliding stability of gravity dams have improved computational accuracy to some extent, they still have some shortcomings. First, most methods use improperly configured machine learning algorithms, failing to effectively uncover deep-seated nonlinear mapping relationships, thus affecting prediction accuracy. Second, existing methods often consider only a single influencing factor, neglecting the combined impact of various geological conditions and load conditions on dam stability, leading to discrepancies between calculated results and actual conditions. Furthermore, the deep sliding mechanism of gravity dams is complex, and many methods lack the ability to accurately describe the location and morphology of the sliding surface. Therefore, a method for calculating the reliability of deep sliding in gravity dams based on optimized limit learning machines is proposed. Summary of the Invention

[0004] In view of the problems of existing gravity dam anti-sliding stability analysis methods based on machine learning algorithms, such as improper parameter settings, neglect of the comprehensive influence of multiple factors, and lack of ability to describe the sliding surface, this invention is proposed.

[0005] Therefore, the problem to be solved by this invention is how to optimize the parameters of the extreme learning machine and comprehensively consider various influencing factors, thereby improving the accuracy of the calculation of the deep sliding reliability of gravity dams.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] In a first aspect, embodiments of the present invention provide a method for calculating the deep sliding reliability of gravity dams based on optimized extreme learning machine (ELM), comprising the following steps: converting a set of input weights and biases of the ELM into SHPSO particle positions x. i The fitness function of the SHPSO particle is the mean square error (MSE) obtained from training, i.e., the SHPSO particle position x. i The relevant formulas are as follows:

[0008] x i =[w 11 ,w 12 ,...,w 1n ,...,w k1 ,w k2 ,...,w kn ,b1,b2,...,b k ]

[0009] Among them, w kn b represents the weight between the k-th hidden layer node and the n-th input layer node. k This is the bias of the k-th hidden layer node.

[0010] Randomly select a portion of the given sample set as the training set and the remainder as the test set; determine the parameters, setting the population size, maximum number of iterations, search space range, search space dimension, and the number of hidden layer nodes and activation function of the ELM algorithm; initialize the particle position x. i and particle velocity v i The Extreme Learning Machine (ELM) is invoked to calculate the fitness of each particle and initialize individual optimal values. Based on the fitness values ​​of each particle, the particles are divided into elite particles, ordinary particles, and inferior particles. Hierarchical learning is then performed on the divided particles to update the particle positions x. i Particle velocity v i The algorithm calculates the particle fitness value; determines whether the individual optimal value among elite particles has been improved and updates the individual optimal value; simultaneously determines whether the fitness evaluation count has reached the maximum number of evaluations, and obtains the input layer weights and biases based on the optimal individual to construct an optimized Extreme Learning Machine (ELM) model; uses multi-strategy fusion to improve the particle swarm optimization algorithm SHPSO to find the optimal parameters of the ELM model; and uses the test set to verify the generalization ability of the optimized ELM model.

[0011] As a preferred embodiment of the method for calculating the deep sliding reliability of gravity dams using the optimized extreme learning machine described in this invention, the fitness evaluation count includes the following formula: when the fitness evaluation count reaches the maximum number of evaluations, the individual optimal value is output, i.e., the formula for updating the individual optimal values ​​of all particles is as follows:

[0012]

[0013] Where, p besti Let be the individual optimal value for particle i. Let be the fitness value in the (t+1)th iteration. Let f(p) be the fitness value in the t-th iteration. besti ) represents the fitness value of particle i as its optimal value.

[0014] If the fitness evaluation count does not reach the maximum number of evaluations, the particles are re-divided.

[0015] As a preferred embodiment of the method for calculating the deep sliding reliability of gravity dams using the optimized extreme learning machine (ELM) of the present invention, the optimized extreme learning machine (ELM) model includes a data preprocessing module, a parameter optimization module, and a prediction module; the data preprocessing module is used for data normalization to eliminate the influence of numerical magnitude; the parameter optimization module uses a multi-strategy fusion improved particle swarm optimization algorithm (SHPSO) to find the optimal parameters of the extreme learning machine (ELM); the prediction module is used to input the required data into the optimized extreme learning machine (ELM) model and output predicted values.

[0016] As a preferred embodiment of the gravity dam deep sliding reliability calculation method using the optimized extreme learning machine described in this invention, the multi-strategy fusion improved particle swarm optimization algorithm SHPSO includes the following steps: updating particle velocity and position using an adaptively changing strategy AW with inertial weights, as shown in the following update formula:

[0017]

[0018] Where u(i) is the inertia weight direction change coefficient, and rand is a random number. Let be the fitness value in the (t+1)th iteration. Let be the fitness value in the t-th iteration.

[0019] Based on the fitness value of the particles after each iteration, the direction of inertia weight is adaptively adjusted, thereby changing the direction of particle motion; based on the particle fitness ranking, the particles are divided into dominant, normal and inferior layers, and an adaptive hierarchical learning strategy is adopted for the characteristics of particles in each layer; differential mutation is performed on the particle swarm type that is dominant.

[0020] As a preferred embodiment of the method for calculating the deep sliding reliability of a gravity dam using the optimized extreme learning machine described in this invention, the differential mutation includes: if the fitness value of the (t+1)th iteration is greater than the fitness value under the tth iteration, then it is determined that the fitness value of elite particle i under the (t+1)th iteration has not improved, and the flight direction of the elite particle deviates from the actual individual optimal value. By changing the direction of the inertial weight by setting the inertial weight direction coefficient to a negative random number, the elite particle flies in the opposite direction of the current motion in the next iteration; if the fitness value of the (t+1)th iteration is greater than the fitness value under the tth iteration, then it is determined that the fitness value of elite particle i under the (t+1)th iteration has not improved, and the flight direction of elite particle i deviates from the actual individual optimal value. The fitness value is less than or equal to the fitness value at the t-th iteration. Then, the inertial weight direction coefficient is set to 1, and the strategy AW is adaptively changed through the inertial weight to make the elite particles continue to fly along the current velocity direction.

[0021] As a preferred embodiment of the method for calculating the deep sliding reliability of gravity dams using the optimized extreme learning machine described in this invention, the construction process of the optimal ELM model includes the following steps: obtaining a sample set and normalizing it; inputting the normalized sample set into the extreme learning machine (ELM), using the mean squared error (MSE) as the fitness evaluation function of the extreme learning machine (ELM), i.e., the relevant formula of the fitness evaluation function is as follows:

[0022]

[0023] Where N is the number of samples, t i Let i be the actual value corresponding to the i-th sample. Let be the simulated predicted value of the i-th sample.

[0024] Based on the optimal parameters, a multi-strategy fusion improved particle swarm optimization algorithm is used to find the optimal weights and biases of the ELM model, and the optimal ELM model is constructed; n is extracted. s Given a sample of random variable X = (x1, x2, ..., x6), extract n samples based on the variance, mean, and distribution type of the random variable using MATLAB functions for each distribution type. s Group samples; input random variable samples into the optimal ELM model to predict n s Group function values; statistical prediction results of the optimal ELM model; the prediction results include failure rate and reliability, i.e., the relevant specific formulas are as follows:

[0025]

[0026] Among them, P f For failure rate, n f n represents the total number of predicted results that are less than zero. s P represents the total number of predicted results greater than zero. r For reliability.

[0027] Secondly, embodiments of the present invention provide a gravity dam deep sliding reliability calculation system based on optimized extreme learning machine, comprising: an acquisition module for acquiring basic information of the gravity dam; a construction module for optimizing the extreme learning machine by improving the particle swarm optimization algorithm SHPSO through multi-strategy fusion and constructing an optimized extreme learning machine ELM model; and a calculation module for constructing an optimal ELM model based on the optimized extreme learning machine ELM model and calculating the deep sliding reliability of the gravity dam.

[0028] Thirdly, embodiments of the present invention provide a computer device, including a memory and a processor, wherein the memory stores a computer program, wherein: when the computer program instructions are executed by the processor, they implement the steps of the method for calculating the deep sliding reliability of gravity dams using an optimized extreme learning machine as described in the first aspect of the present invention.

[0029] Fourthly, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program instructions are executed by a processor, they implement the steps of the method for calculating the deep sliding reliability of a gravity dam using an optimized extreme learning machine as described in the first aspect of the present invention.

[0030] The beneficial effects of this invention are as follows: This invention lays the foundation for calculation by obtaining basic information about gravity dams; it uses the Extreme Learning Machine (ELM) parameters as the optimization target and optimizes the ELM parameters using the multi-strategy fusion improved particle swarm optimization algorithm (SHPSO), thereby improving the prediction accuracy and generalization ability of the ELM model; it constructs an optimal model based on the optimal parameters of the optimized ELM model, and extracts random samples for input calculation, which can accurately obtain the deep sliding failure rate and reliability of gravity dams, providing accurate data support for the anti-sliding stability analysis of dams and making up for the shortcomings of existing methods. Attached Figure Description

[0031] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0032] Figure 1 The flowchart of the optimized Extreme Learning Machine (ELM) model for calculating the deep sliding reliability of gravity dams using the optimized Extreme Learning Machine in Example 1 is shown.

[0033] Figure 2 A cross-sectional view of a gravity dam for calculating the deep sliding reliability of a gravity dam using the optimized extreme learning machine in Example 1.

[0034] Figure 3 The comparison results of the optimized extreme learning machine (ELM) model for deep anti-sliding of gravity dams and the optimal ELM model are presented for Example 1, which is based on the calculation method of deep sliding reliability of gravity dams using the optimized extreme learning machine.

[0035] Figure 4 The image shows the error of the actual value of the optimized Extreme Learning Machine (ELM) model before optimization in Example 1, which is used to calculate the reliability of deep sliding of a gravity dam using an optimized Extreme Learning Machine.

[0036] Figure 5 Example 1 shows the error diagram of the predicted value of the optimized Extreme Learning Machine (ELM) model after optimizing the method for calculating the reliability of deep sliding gravity dams using the optimized Extreme Learning Machine. Detailed Implementation

[0037] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0038] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0039] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0040] Example 1

[0041] Reference Figures 1-2 This is the first embodiment of the present invention, which provides a method for calculating the deep sliding reliability of gravity dams based on optimized limit learning machines, including:

[0042] S1: Obtain basic information about gravity dams.

[0043] Specifically, a certain concrete gravity dam is a Class II structure. The dam's cross-section is shown below. Figure 2 As shown, the dam crest height is 70m, the dam crest width is 7m, the water depth in front of the dam is 65m, the width of the foundation surface at the dam base is 45.5m, the downstream dam slope ratio is 1:0.8, the curtain wall is 10m from the dam heel, and structural planes AB and BC are two weak structural planes in the bedrock, each with a width of 40cm. The angles between the two weak structural planes and the horizontal plane are and , respectively. Taking the dam heel as the origin, the coordinates of point A are (-5,0), the coordinates of point B are (48.25,-14.27), and the coordinates of point C are (94.93,0).

[0044] S2: Improve the particle swarm optimization algorithm SHPSO by multi-strategy fusion to optimize the extreme learning machine and construct the optimized extreme learning machine ELM model.

[0045] Specifically, constructing an optimized Extreme Learning Machine (ELM) model includes the following steps: The ELM's input weights and biases are set as the SHPSO particle positions x. i The fitness function of the SHPSO particle is the mean square error (MSE) obtained during training; the position x of the SHPSO particle... i The relevant formulas are as follows:

[0046] x i =[w 11 ,w 12,...,w 1n ,...,w k1 ,w k2 ,...,w kn ,b1,b2,...,b k ]

[0047] Among them, w kn b represents the weight between the k-th hidden layer node and the n-th input layer node. k This is the bias of the k-th hidden layer node.

[0048] Furthermore, a portion of the given sample set is randomly selected as the training set, and the remainder is used as the test set; parameters are determined, including setting the population size, maximum number of iterations, search space range, search space dimension, and the number of hidden layer nodes and activation function of the SHPSO algorithm; particle position x is initialized. i and particle velocity v i The Extreme Learning Machine (ELM) is invoked to calculate the fitness of each particle and initialize individual optimal values. Based on the fitness values ​​of each particle, the particles are divided into elite particles, ordinary particles, and inferior particles. Hierarchical learning is then performed on the divided particles to update the particle positions x. i Particle velocity v i And particle fitness values. Determine whether the individual optimal value of elite particles has been improved and update the individual optimal value; at the same time, determine whether the fitness evaluation count has reached the maximum number of evaluations, and obtain the input layer weights and biases based on the optimal individual to construct an optimized Extreme Learning Machine (ELM) model; use multi-policy fusion to improve the particle swarm optimization algorithm (SHPSO) to find the optimal parameters of the ELM model; use the test set to verify the generalization ability of the optimized ELM model.

[0049] Specifically, the number of fitness evaluations includes the following: when the maximum number of fitness evaluations is reached, the individual optimal value is output. The relevant formula for updating the individual optimal values ​​of all particles is as follows:

[0050]

[0051] Where, p besti Let be the individual optimal value for particle i. Let be the fitness value in the (t+1)th iteration. Let f(p) be the fitness value in the t-th iteration. besti ) represents the fitness value of particle i as its optimal value.

[0052] Furthermore, if the fitness evaluation count does not reach the maximum number of evaluations, the particles are re-divided.

[0053] Specifically, the biases of the hidden layer nodes are shown in Table 1.

[0054] Table 1. Weights of Hidden Layer Nodes

[0055]

[0056] Furthermore, the weights from hidden layer nodes to output layer nodes are shown in Table 2.

[0057] Table 2. Bias Table for Hidden Layer Nodes

[0058] Hidden layer nodes bias Hidden layer nodes bias 1 0.687 6 0.487 2 0.128 7 0.026 3 0.001 8 0.999 4 1.000 9 0.334 5 0.149 10 0.305

[0059] Furthermore, the multi-strategy fusion improved particle swarm optimization algorithm SHPSO includes the following steps: Adaptively changing the inertia weight strategy AW to update particle velocity and position, with the update formula as follows:

[0060]

[0061] Where u(i) is the inertia weight direction change coefficient, and rand is a random number. Let be the fitness value in the (t+1)th iteration. Let be the fitness value in the t-th iteration.

[0062] Specifically, based on the fitness value of the particles after each iteration, the direction of inertia weight is adaptively adjusted, thereby changing the direction of particle motion; based on the particle fitness ranking, particles are divided into dominant, normal, and inferior layers, and an adaptive hierarchical learning strategy is adopted for the characteristics of particles in each layer; differential mutation is performed on the particle swarm type that is dominant.

[0063] It should be noted that the random variables and function are determined; six random factors X = (x1,...,x6) affecting the deep anti-sliding properties of the gravity dam are considered, namely: friction coefficient of bedrock I, cohesion of bedrock I, friction coefficient of structural plane AB, cohesion of structural plane AB, friction coefficient of structural plane BC, and cohesion of structural plane BC. The gravity dam profile is shown in [reference needed]. Figure 2 The distribution characteristics of the values ​​of each factor are shown in Table 1.

[0064] Table 3. Distribution characteristics of values ​​for each factor

[0065] random factors mean Standard deviation Distribution type Bedrock I friction coefficient 1.1 0.22 normal distribution Bedrock I Cohesion / MPa 1.1 0.33 normal distribution Friction coefficient of structural surface AB 0.35 0.07 normal distribution AB cohesion of structural surface / MPa 0.05 0.015 Log-normal Friction coefficient of structural surface BC 0.45 0.09 normal distribution BC cohesion of structural plane / MPa 0.1 0.03 Log-normal

[0066] Furthermore, differential mutation includes: if the fitness value in the (t+1)th iteration is greater than the fitness value in the tth iteration, then it is determined that the fitness value of elite particle i has not improved in the (t+1)th iteration, and the flight direction of the elite particle deviates from the actual individual optimal value. The inertial weight direction coefficient is changed by setting it to a negative random number, causing the elite particle to fly in the opposite direction in the next iteration; if the fitness value in the (t+1)th iteration... The fitness value is less than or equal to the fitness value at the t-th iteration. Then, the inertial weight direction coefficient is set to 1, and the strategy AW is adaptively changed through the inertial weight to make the elite particles continue to fly along the current velocity direction.

[0067] Furthermore, the optimized Extreme Learning Machine (ELM) model includes a data preprocessing module, a parameter optimization module, and a prediction module. The data preprocessing module is used for data normalization to eliminate the influence of numerical magnitude. The parameter optimization module uses a multi-strategy fusion improved particle swarm optimization algorithm (SHPSO) to find the optimal parameters for the Extreme Learning Machine (ELM). The prediction module is used to input the required data into the optimized Extreme Learning Machine (ELM) model and output predicted values.

[0068] S3: Based on the optimized Extreme Learning Machine (ELM) model, construct the optimal ELM model and calculate the reliability of deep sliding of the gravity dam.

[0069] Specifically, the optimal ELM model includes the following steps: obtaining a sample set and normalizing it; inputting the normalized sample set into the Extreme Learning Machine (ELM), using the Mean Squared Error (MSE) as the fitness evaluation function of the ELM, i.e., the relevant formula for the fitness evaluation function is as follows:

[0070]

[0071] Where N is the number of samples, t i Let i be the actual value corresponding to the i-th sample. Let be the simulated predicted value of the i-th sample.

[0072] Furthermore, based on the optimal parameters, a multi-strategy fusion improved particle swarm optimization algorithm is used to find the optimal weights and biases of the ELM model, and to construct the optimal ELM model; n is extracted. s Given a sample of random variable X = (x1, x2, ..., x6), extract n samples based on the variance, mean, and distribution type of the random variable using MATLAB functions for each distribution type. s Group samples; input random variable samples into the Extreme Learning Machine (ELM) model to predict n s Group function values; statistical analysis of SHPSO-ELM prediction results; prediction results include failure rate and reliability, the specific formulas are as follows:

[0073]

[0074] Among them, P f For failure rate, n f n represents the total number of predicted results that are less than zero. s P represents the total number of predicted results greater than zero. r For reliability.

[0075] Furthermore, this embodiment also provides a gravity dam deep sliding reliability calculation system based on optimized extreme learning machine, including: an acquisition module for acquiring basic information about the gravity dam; a construction module for optimizing the extreme learning machine by improving the particle swarm optimization algorithm SHPSO through multi-strategy fusion and constructing an optimized extreme learning machine ELM model; and a calculation module for constructing an optimal ELM model based on the optimized extreme learning machine ELM model and calculating the deep sliding reliability of the gravity dam.

[0076] This embodiment also provides a computer device applicable to the optimization of the extreme learning machine for calculating the deep sliding reliability of gravity dams, including a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the optimization of the extreme learning machine for calculating the deep sliding reliability of gravity dams as proposed in the above embodiment.

[0077] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0078] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, performs the following steps: acquiring basic information about the gravity dam; optimizing the Extreme Learning Machine (ELM) using the Multi-Strategy Fusion Improvement Particle Swarm Optimization (SHPSO) algorithm and constructing an optimized ELM model; and constructing an optimal ELM model based on the optimal parameters of the optimized ELM model to calculate the deep sliding reliability of the gravity dam.

[0079] In summary, this invention lays the foundation for calculations by acquiring basic information about the gravity dam; it uses the Extreme Learning Machine (ELM) parameters as the optimization objective and optimizes the ELM parameters using a multi-strategy fusion-improved particle swarm optimization algorithm (SHPSO) to improve the prediction accuracy and generalization ability of the ELM model; based on the optimal parameters of the optimized ELM model, it constructs an optimal model and extracts random samples for input calculation, which can accurately obtain the deep sliding failure rate and reliability of the gravity dam, providing accurate data support for the anti-sliding stability analysis of the dam body and making up for the shortcomings of existing methods.

[0080] Example 2

[0081] Reference Figures 3-5 This is the second embodiment of the present invention, which provides a method for calculating the reliability of deep sliding of gravity dams based on optimized limit learning machine. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiment.

[0082] Specifically, to verify the effectiveness of this invention, the results of the optimized Extreme Learning Machine (ELM) model before optimization and the optimal ELM model after optimization were compared. 200 sets of data were substituted into the optimized ELM model for training. The optimized ELM model has one input layer, one hidden layer, and one output layer. The input layer has 6 neurons, the optimal number of hidden layer neurons is 10, and the output layer has 1 neuron. The sample set is divided into a training set and a test set, each accounting for 50% of the dataset samples. The SHPSO algorithm has a population size of 40, a mutation probability of 0.2, 1000 iterations, and uses the Sigmoid function as the activation function.

[0083] Furthermore, as shown in Table 4, the results of the optimal ELM model and the optimized extreme learning machine ELM model are compared. The optimized extreme learning machine ELM model has a larger regression coefficient on the test set, indicating that the optimized extreme learning machine ELM model has a better generalization effect. It can be seen that the MSE and MAPE of the optimized extreme learning machine ELM model on both the training and test sets are smaller than those of the ELM model.

[0084] Table 4 Comparison of Results

[0085] Model MSE_train MAPE_train MSE_test MAPE_test R_test Optimize the Extreme Learning Machine (ELM) model 6.84E-05 2.90E-03 2.30E-03 1.00-02 0.98352 Optimal ELM Model 2.40E-03 1.80E-02 4.70E-03 2.44E-02 0.96567

[0086] Furthermore, such as Figure 3 As shown in the figure, the error between the predicted and actual values ​​of the ELM model on the test set before and after optimization is compared. Figure 4 Optimize the Extreme Learning Machine (ELM) model and plot the relationship between the true and predicted values ​​on the test set of the optimal ELM model. Figure 5 It can also be directly seen that the data points of the optimized Extreme Learning Machine (ELM) model are more concentrated on the Y=T line.

[0087] First, determine the random variable and the function, based on... Figure 4 We obtained the mean, standard deviation, and distribution type of each factor and sampled 2 million sets of data using MATLAB. These 2 million sets of samples were then fed into the constructed Extreme Learning Machine (ELM) model to predict 2 million function values. A predicted value less than zero indicates one structural failure. The number of structural failures was counted, and the failure probability was calculated to be 0.00072%, with a reliability index of 4.320. The Monte Carlo method of the LHS-BP surrogate model yielded a failure probability of 0.00065% and a reliability index of 4.360. The absolute error and relative error of the reliability index calculation results for the two methods were 0.040 and 0.925%, respectively, indicating that the results from the two methods were not significantly different. If the result calculated by the Monte Carlo method of the LHS-BP surrogate model is taken as the exact solution, it shows that the Monte Carlo method of the Extreme Learning Machine (ELM) model achieves both high accuracy and improved computational efficiency. Deep sliding instability of gravity dams is classified as a Class II failure according to the standard. The concrete gravity dam in this embodiment of the invention is a Class II structure, and the corresponding target reliability index is 3.7. The calculated reliability index is greater than the standard value, indicating that the gravity dam meets the requirements for deep sliding stability.

[0088] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for calculating the reliability of deep sliding gravity dams based on optimized extreme learning machine, characterized in that: include, Obtain basic information about gravity dams; By improving the particle swarm optimization algorithm SHPSO through multi-strategy fusion, an optimized extreme learning machine (ELM) model is constructed. Based on the optimal parameters of the optimized Extreme Learning Machine (ELM) model, an optimal ELM model is constructed, and the reliability of deep sliding of the gravity dam is calculated. The process of constructing the optimized Extreme Learning Machine (ELM) model includes the following steps: The Extreme Learning Machine (ELM) uses a set of input weights and biases as the SHPSO particle position x. i The fitness function of the SHPSO particle is the mean square error (MSE) obtained from training, i.e., the SHPSO particle position x. i The relevant formulas are as follows: x i =[w 11 ,w 12 ,...,w 1n ,...,w k1 ,w k2 ,...,w kn ,b1,b2,...,b k ] Among them, w kn b represents the weight between the k-th hidden layer node and the n-th input layer node. k This is the bias of the kth hidden layer node; A portion of the given sample set is randomly selected as the training set, and the remaining portion is used as the test set. Determine the parameters, including the population size, maximum number of iterations, search space range, search space dimension, and the number of hidden layer nodes and activation function of the SHPSO algorithm; Initialize particle position x i and particle velocity v i ; The Extreme Learning Machine (ELM) is invoked to calculate the fitness of each particle and initialize the individual optimal value. Based on the fitness value of each particle, the particles are divided into elite particles, ordinary particles, and inferior particles. Perform hierarchical learning on the divided particles and update the particle position x. i Particle velocity v i and particle fitness value; Determine whether the individual optimal value of elite particles has improved, and update the individual optimal value accordingly; Simultaneously, it is determined whether the fitness evaluation count has reached the maximum number of evaluations, and the input layer weights and biases are obtained based on the optimal individual to construct an optimized extreme learning machine (ELM) model; The optimal parameters of the Extreme Learning Machine (ELM) are found by improving the particle swarm optimization algorithm SHPSO using multi-strategy fusion. The generalization ability of the optimized Extreme Learning Machine (ELM) model was verified using a test set. The multi-strategy fusion improved particle swarm optimization algorithm SHPSO includes the following steps: An adaptive inertial weighting strategy (AW) is used to update particle velocity and position. The update formula is as follows: Where u(i) is the inertia weight direction change coefficient, and rand is a random number. Let be the fitness value in the (t+1)th iteration. This represents the fitness value in the t-th iteration. Based on the particle's fitness value after each iteration, the inertia weight direction is adaptively adjusted, thereby changing the particle's motion direction; Based on particle fitness ranking, particles are divided into advantageous, normal and disadvantageous layers, and an adaptive hierarchical learning strategy is adopted for the characteristics of particles in each layer. Differential mutation is performed on the layer where the particle swarm type is dominant.

2. The method for calculating the deep sliding reliability of gravity dams using optimized extreme learning machines as described in claim 1, characterized in that: The number of fitness evaluations includes, When the fitness evaluation count reaches the maximum number of evaluations, the individual optimal value is output. The relevant formula for updating the individual optimal values ​​of all particles is as follows: Where, p besti Let be the individual optimal value for particle i. Let be the fitness value in the (t+1)th iteration. Let f(p) be the fitness value in the t-th iteration. besti ) represents the fitness value of particle i, which is the optimal value for that individual. If the fitness evaluation count does not reach the maximum number of evaluations, the particles are re-divided.

3. The method for calculating the deep sliding reliability of gravity dams using optimized extreme learning machines as described in claim 2, characterized in that: The optimized Extreme Learning Machine (ELM) model includes a data preprocessing module, a parameter optimization module, and a prediction module. The data preprocessing module is used for data normalization to eliminate the influence of numerical magnitude. The parameter optimization module uses a multi-strategy fusion improved particle swarm optimization algorithm (SHPSO) to find the optimal parameters for the Extreme Learning Machine (ELM). The prediction module is used to input the required data into the optimized Extreme Learning Machine (ELM) model and output predicted values.

4. The method for calculating the deep sliding reliability of gravity dams using optimized extreme learning machines as described in claim 3, characterized in that: The differential variation includes, If the fitness value in the (t+1)th iteration is greater than the fitness value in the tth iteration, then it is determined that the fitness value of the elite particle i has not improved in the (t+1)th iteration, and the flight direction of the elite particle deviates from the actual individual optimal value. By setting the inertial weight direction coefficient to a negative random number to change the inertial weight direction, the elite particle will fly in the opposite direction of the current motion in the next iteration. If the fitness value of the (t+1)th iteration The fitness value is less than or equal to the fitness value at the t-th iteration. Then, the inertial weight direction coefficient is set to 1, and the strategy AW is adaptively changed through the inertial weight to make the elite particles continue to fly along the current velocity direction.

5. The method for calculating the deep sliding reliability of gravity dams using optimized extreme learning machines as described in claim 1, characterized in that: The process of constructing the optimal ELM model includes the following steps: Obtain the sample set and normalize it; The normalized sample set is input into the Extreme Learning Machine (ELM), and the mean squared error (MSE) is used as the fitness evaluation function of the ELM. The relevant formula for the fitness evaluation function is as follows: Where N is the number of samples, t i Let i be the actual value corresponding to the i-th sample. Let be the simulated predicted value of the i-th sample; Based on the optimal parameters, the optimal weights and biases of the ELM are found by using a multi-strategy fusion improved particle swarm optimization algorithm to construct the optimal ELM model. Extract n s Given a sample of random variable X = (x1, x2, ..., x6), extract n samples based on the variance, mean, and distribution type of the random variable using MATLAB functions for each distribution type. s Group samples; Input random variable samples into the optimal ELM model to predict n. s Group function values; Statistically analyze the prediction results of the optimal ELM model; The prediction results include failure rate and reliability, and the specific formulas are as follows: Among them, P f For failure rate, n f n represents the total number of predicted results that are less than zero. s P represents the total number of predicted results greater than zero. r For reliability.

6. A system for calculating the reliability of deep sliding gravity dams based on optimized limit learning machines, and a method for calculating the reliability of deep sliding gravity dams based on optimized limit learning machines according to any one of claims 1 to 5, characterized in that: include, The acquisition module is used to obtain basic information about gravity dams; The building block is used to improve the particle swarm optimization algorithm SHPSO to optimize the extreme learning machine through multi-strategy fusion, and to build an optimized extreme learning machine (ELM) model. The calculation module is used to construct the optimal ELM model based on the optimized Extreme Learning Machine (ELM) model and calculate the deep sliding reliability of the gravity dam.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the method for calculating the deep sliding reliability of gravity dams using the optimized extreme learning machine as described in any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the method for calculating the deep sliding reliability of gravity dams using the optimized extreme learning machine as described in any one of claims 1 to 5.

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