A method for constructing a numerical model of a bridge pile foundation with uneven distribution of structural planes

Abstract

The application relates to the technical field of bridge engineering and discloses a bridge pile foundation numerical model construction method for uneven distribution of structural surfaces, which comprises the following steps: collecting and arranging a bridge pile foundation design database under uneven structural surfaces; classifying and dividing all data samples and carrying out pretreatment; establishing an NAR dynamic neural network structure, initializing neural network related parameters; adopting a Logistic chaotic mapping to initialize a beetle population; and obtaining a current updated optimal population position through subsequent processing. The bridge pile foundation numerical model construction method for uneven distribution of structural surfaces is combined with an NAR dynamic neural network structure, a chaotic mapping initialized population and a beetle algorithm, a calculation model most conforming to the bridge pile foundation design database under uneven structural surfaces is finally determined, the calculation model is high in accuracy and efficiency, and economic cost is saved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bridge engineering, and particularly relates to a bridge pile foundation numerical model construction method for uneven distribution of structural surfaces. BACKGROUND

[0002] With the development of transportation in China, more and more highways and railways are built in mountainous areas, such as Shanghai-Ruili highway Shaohuai section, Guangdong-Hainan highway Changchun-Liaoning section, Baomao highway Jihuai section and Zhanghua connecting line, Shanghai-Chengdu section, etc. However, the topography and geological conditions in mountainous areas are complex, with large ground elevation difference, frequent slope change and large longitudinal slope, which bring more challenges to engineering construction. In mountainous engineering construction, bridge engineering is mostly built across deep valleys or along steep slopes, forming a complex system of foundation and slope. Especially if the slope is in an unstable state, the pile foundation built on it not only bears the combined load transferred to the top of the pile by the superstructure, but also bears the landslide thrust caused by the potential sliding deformation of the slope. However, most of the pile foundation research on slopes starts from soil slopes, and for rock slopes, especially for rock masses with uneven distribution of structural planes, the design of pile foundation is more complex. For complex rock masses, the uncertainty of structural plane distribution makes the time and economic cost of pile foundation design and construction greatly increased. In addition, the design calculation and scheme selection are still in the stage of manual operation, and the number of parameters considered increases the error rate of manual operation, so a large safety factor is often taken in the design to ensure the long-term stability of the foundation and superstructure, but this causes great waste of materials and cost. Structural plane rock mass usually shows different structural plane occurrence and structural plane distribution density at different positions, and the beetle algorithm can efficiently calculate the distribution characteristics of structural planes. Artificial neural network is a technical reproduction of biological neural network in a certain simplified sense. Biological neural network mainly refers to the neural network of human brain, which is the material basis of human thinking. The function of thinking is located in the cerebral cortex, which contains about 1011 neurons, and each neuron is connected to about 103 other neurons through synapses, forming a highly complex and flexible dynamic network. The main task of neural network is to build practical artificial neural network model according to the principle of biological neural network and the needs of practical application, design corresponding learning algorithm, simulate certain intelligent activities of human brain, and then realize it technically to solve practical problems. Neural network can perform large-scale parallel processing, distributed storage, elastic topology, high redundancy and nonlinear operation. Therefore, it has high computing speed, strong associative ability, strong adaptability, strong fault tolerance and self-organization ability. Neural network has obtained important applications in data compression, image processing, vector coding, error control (error correction and error detection coding), adaptive signal processing, adaptive equalization, signal detection, pattern recognition, etc.China is in the stage of rapid development of computers, therefore, the establishment of the model of the slope pile foundation containing the structural plane based on the algorithm of the blaberus can not only greatly reduce the cost of manpower, reduce the error rate in complex design, reduce the incidence of disasters, protect the safety of life and property of relevant personnel, greatly save the construction cost, and meet the green and sustainable development concept of China.

[0003] The Chinese patent document with publication number CN116258972B and publication date of 2023-08-01 discloses a rock high and steep slope structural plane extraction method based on deep learning, including the following steps: 1, collecting three-dimensional point cloud data of the rock high and steep slope structural plane, and preprocessing the three-dimensional point cloud data; 2, using the Knnsearch function to search for the nearest points of the three-dimensional point cloud data, obtaining an initial nearest point set; 3, performing coplanar testing on the initial nearest point set to obtain a nearest point set; 4, performing plane fitting on the nearest point set to obtain a plane fitting image, and calculating the normal vector of the fitted plane; 5, taking the plane fitting image as a training set sample; 6, constructing a VGGNet model based on the Softmax function; 7, training the training set sample using the VGGNet model to obtain the rock high and steep slope structural plane distribution, and the rock high and steep slope structural plane occurrence and rock high and steep slope structural plane distribution.

[0004] The Chinese patent document with publication number CN117540476A and publication date of 2024-02-09 discloses a method and system for predicting the spatial distribution of structural planes and their adverse combinations in extremely hard rock tunnels, mainly including: collecting regional geological data and exploration data, preliminarily delineating structural planes and their adverse combination development segments, selecting a target extremely hard rock tunnel as a prediction object, and determining the tunnel body orientation and the size of the tunnel face; based on the selected target extremely hard rock tunnel and related exploration data, extracting the structural plane occurrence and characteristic data within a preset range in front of the tunnel face; inputting the extracted structural plane occurrence and characteristic data into a pre-established prediction model to generate a three-dimensional geological model, and assigning values to the pre-established evaluation index system according to the input structural plane occurrence and characteristic data, based on the pre-established risk level standard, grading the risk of the spatial distribution of structural planes and their adverse combinations according to the values of each evaluation index, and according to the grading results, prompting the high-risk areas of falling and collapsing in the three-dimensional geological model to obtain the prediction results.

[0005] Chinese patent document CN115330975B, published on May 23, 2023, discloses a three-dimensional random rough structural surface network model, its construction method, and apparatus. Based on the spatial distribution morphology of structural surfaces and a survey of structural surface information, this invention utilizes fractal geometry principles to model a three-dimensional distribution network of rock mass structural surfaces. It focuses on proposing a method for constructing complex, undulating three-dimensional structural surfaces under three-dimensional spatial distribution conditions. This represents a three-dimensional extension of the current two-dimensional rough discrete structural surface network model, expanding the research field of three-dimensional structural surface modeling and the mechanical properties of jointed rock masses.

[0006] This invention uses MATLAB to export three-dimensional digital models and provides point cloud data output of three-dimensional structural surfaces. It can provide an interface for numerical calculation of particle flow discrete element method. It can be directly extended to the field of 3D printing technology of three-dimensional complex jointed rock mass, provide a model for indoor similarity test, and provide characterization methods and models for more refined study of the mechanical properties of three-dimensional jointed rock mass. Summary of the Invention

[0007] The purpose of this invention is to provide a method for constructing a numerical model of bridge pile foundations with unevenly distributed structural surfaces. This method combines a NAR dynamic neural network structure, a chaotic mapping initialization population, and a dung beetle algorithm to ultimately determine the computational model that best fits the bridge pile foundation design database under uneven structural surfaces. This computational model has high accuracy and efficiency, while also saving economic costs.

[0008] To achieve the above objectives, this invention provides a method for constructing a numerical model of bridge pile foundations with non-uniformly distributed structural surfaces, comprising the following steps:

[0009] Step 1: Collect and organize the bridge pile foundation design database under non-uniform structural planes, including engineering geological conditions, surrounding rock grade, engineering dimensions, and ground settlement around the pile foundation in different regions;

[0010] Step 2: Classify and divide all data samples, and preprocess them. Select 75% of the samples as the training set and 25% of the samples as the test set.

[0011] Step 3: Establish the NAR dynamic neural network structure and initialize the relevant parameters of the neural network; the neural network includes an input layer, an output layer, a hidden layer, and a lag layer. Data enters from the input layer, enters the hidden layer and the lag layer, and after training, transmission, and learning, it reaches the output layer to obtain the prediction result;

[0012] Step 4: Initialize the population using chaotic mapping. The dung beetle population is initialized using Logistic chaotic mapping.

[0013] Step 5: Calculate the initial fitness of the dung beetle population;

[0014] Step 6: Update the locations of the four types of dung beetles, including the rolling dung beetle, the hatching dung beetle, the small dung beetle, and the thieving dung beetle, updating them according to their respective rules;

[0015] Step 7: Action Mutation Strategy; In order for each dung beetle to perform 4 actions, the time change is simulated by the number of iterations, and action mutation is performed once every M iterations;

[0016] Step 8: Introduce adaptive weights to iteratively update the position of the dung beetle; adopt the spiral ascending search method of iterative optimization in the whale optimization algorithm to increase the global search capability and diversity of the dung beetle, and introduce adaptive weight factors;

[0017] Step 9: Update the spatial location of dung beetles by randomly disturbing those in the best positions;

[0018] Step 10: To improve the algorithm's optimization capability and escape local optima, Gaussian mutation and Gaussian perturbation are introduced;

[0019] Step 11: Obtain the current updated optimal population position. If the new position is better than the old position in the previous iteration, perform the update operation; otherwise, return to step 3 and continue the iteration operation until the condition is met.

[0020] Step 12: Output the optimal delay order and number of hidden layers, and feed them back to the NAR dynamic neural network for retraining, testing, prediction, and output of results.

[0021] Furthermore, in step 4, a Logistic chaotic mapping is used to initialize the dung beetle population, including the population size, number of iterations, mutation strategy, maximum number of iterations, and adaptive weight factor. The Logistic chaotic mapping can uniformly distribute the dung beetles in the search space, and finally, a global search is used to obtain the optimal position and its fitness value. The mathematical expression of the Logistic mapping is shown in equation (I).

[0022]

[0023] in, Let be the current iteration state value of the i-th variable, with a value range of [0, 1]. is the state value for the next iteration; μ is the branch parameter that determines whether the Logistic mapping is in a chaotic state, and its value ranges from [0, 4].

[0024] Furthermore, the update rule for the dung beetle in step 6 is as follows:

[0025] During the rolling process, the dung beetle's position update occurs in two ways:

[0026] ① When there are no obstacles, it can be represented as:

[0027] x i (t+1)=x i (t)+α×k×x i (t-1)+b×△x (1)

[0028] △x=|x i (t)-x w | (2)

[0029] Where: t represents the current iteration number; x i (t) represents the position information of the i-th dung beetle in the t-th iteration; k∈(0,0.2] represents the constant of the deviation coefficient; b∈(0,1) is a constant value; α is a natural coefficient assigned the value -1 or 1; X w Indicates the worst position globally;

[0030] ② When there are obstacles: The tangent function is used to simulate the dance behavior to determine a new route. The position update definition for the dung beetle is as follows:

[0031] x i (t+1)=x i (t)+tan(θ)|x i (t)-x i (t-1)| (3)

[0032] Where: θ∈[0,π].

[0033] Furthermore, the update rule for the dung beetle in step 6 is as follows:

[0034] Dung beetles roll their dung balls to a safe place and hide them, providing a safe environment for their offspring. Choosing a suitable egg-laying site is crucial. A boundary selection strategy is used to simulate the egg-laying area of ​​female dung beetles, defined as follows:

[0035] Lb * =max(X * ×(1-R), Lb) (4)

[0036] Ub * =min(X) * ×(1+R), Ub) (5)

[0037] Where: X * Lb represents the current local optimum. * and Ub * These represent the next and previous terms of the spawning region, respectively; R = 1 - t / T max and T max This represents the maximum number of iterations, and Lb and Ub represent the next and previous iterations of the optimization problem, respectively.

[0038] The formula for updating the position of the dung beetle is as follows:

[0039] S i (t+1)=X * +b1×(S i (t)-Lb * )+b2×(S i (t)-Ub * (6)

[0040] Among them: B i (t) represents the position information of the i-th brooding ball in the nth iteration, b1 and b2 represent two independent random variables of size 1×D, and D represents the dimension of the optimization problem.

[0041] Furthermore, the update rule for the dung beetle in step 6 is as follows:

[0042] Dung beetles are newly grown dung beetles foraging in their optimal foraging area, which is defined as:

[0043] Lb b =max(X b ×(1-R), Lb) ( 7 )

[0044] Ub b =min(X) b ×(1+R), Ub) (8)

[0045] Where: X b Lb represents the current local optimum. b and Ub b Let R represent the next and previous bounds of the optimal foraging region, respectively; R = 1 - t / T max and T max This represents the maximum number of iterations, and Lb and Ub represent the next and previous iterations of the optimization problem, respectively.

[0046] The formula for updating the position of the dung beetle is as follows:

[0047] x i (t+1)=x i (t)+C1×(x i (t)-Lb b )+C2×(x i (t)-Ub b (9)

[0048] Where: x i (t) represents the position information of the i-th dung beetle in the nth iteration, C1 represents a random number that follows a normal distribution, and C2 represents a random vector belonging to (0, 1).

[0049] Furthermore, the update rule for the dung beetle in step 6 is as follows:

[0050] The thieving dung beetle steals dung balls from other dung beetles. Let's assume X... b The surrounding area represents the best location for competing for food. During the iteration process, the dung beetle's location information is updated as follows:

[0051] x i (t+1)=X b +S×g×(|x i (t)-X * |+|x i (t)-X b |) (10)

[0052] Where: x i (t) represents the location information of the i-th thief in the nth iteration, g is a random vector of size 1×D that follows a normal distribution, and S represents a constant.

[0053] Furthermore, in step 7, to enable each dung beetle to perform four actions, the number of iterations is used to simulate time changes. Every M iterations, an action mutation is performed, transforming the current action into the behavioral strategy for the next chapter. The population diversity is represented as follows:

[0054]

[0055] in: This represents the optimal value among the local and global optimal solutions.

[0056] Furthermore, the specific location update method in step 8 is as follows:

[0057]

[0058] Where: X i (t+1) represents the updated position of the i-th dung beetle, X best (t) represents the optimal position in the t-th iteration, γ is a uniformly random number in (0,1], and iter max This represents the maximum number of iterations for the population.

[0059] Furthermore, the position update function in step 9 is:

[0060]

[0061] Where: X i (t+1) represents dung beetle X i The position after the (t+1)th move, X i (t) represents dung beetle X i The position after the t-th move, X j (t) represents dung beetle Xj The position after the t-th move, ζ represents the step size factor which is a constant in the range [0,1], and rand is a random factor that follows a uniform distribution in the range [0,1].

[0062] Furthermore, in step 10, Gaussian variation refers to the variation from the mean μ, σ 2 A random number is drawn from the normal distribution and used to replace the parameter variables in the dung beetle algorithm to achieve the purpose of optimizing the algorithm; Gaussian perturbation is used to improve the ability to escape local optima. A small Gaussian perturbation is applied to the optimal position of the individual dung beetle after each iteration to help it escape the local optimum better.

[0063] The fitness value F of the population is expressed as shown in equation (14), where f(X) is the fitness function:

[0064] F=[f(X1)f(X2)…f(X n )] T (14)

[0065] In the formula: X i Let f(X) be the position of the i-th dung beetle. i ) represents the fitness value of an individual dung beetle;

[0066] When f i (Current fitness value of the individual) <f av (Average fitness value), the optimal individual of the population is determined by introducing Gaussian mutation (15), when f i ≥f av By introducing Gaussian perturbation equations (16) and (17), the optimal individuals of the population can be determined. Combining Gaussian mutation and Logistic chaotic mapping can accelerate the convergence speed and evolutionary performance of FA.

[0067] T g =Lo(1+N(0,1))(15)

[0068] In the formula: N(0,1) is a normally distributed random number with an expected value of 0 and a standard deviation of 1; T g The value is calculated by Gaussian mutation after initializing the parameters;

[0069] G b =G(1+Gaussian(μ,σ) 2 ))(16)

[0070]

[0071] Where: G b Let G be the optimal position of the dung beetle in each iteration; G is the fitness of the dung beetle before Gaussian perturbation, Gaussian(μ,σ) 2 The mean is μ and the variance is σ.2 Gaussian function; To determine the optimal fitness of the disturbed dung beetle individual; G t Let be the optimal fitness of the dung beetle individual in the t-th iteration.

[0072] The advantages and positive effects of the numerical model construction method for bridge pile foundations with unevenly distributed structural surfaces described in this invention are as follows:

[0073] 1. Current research on the distribution characteristics of slope rock mass structural surfaces mainly focuses on the selection of algorithms. The distribution of structural surfaces on slopes for bridge pile foundations is the basis for exploring the bearing capacity and stress deformation of pile foundations. This invention considers the influence of non-uniform rock mass structural surfaces and establishes a numerical model of pile foundations on slopes based on the Shenjiang network. It combines the NAR dynamic neural network structure, chaotic mapping initialization population and dung beetle algorithm to finally determine the numerical calculation model of non-uniform structural surface pile foundations that best fits the bridge pile foundation design database under non-uniform structural surfaces, resulting in better accuracy.

[0074] 2. Regarding the distribution of structural surfaces within the rock strata of the sloping bridge pile foundation, this invention uses Logistic chaotic mapping to initialize the dung beetle population, which can increase the diversity of the population, improve the global search capability and convergence speed of the algorithm, thereby effectively improving the solution efficiency and accuracy of the algorithm; at the same time, Gaussian mutation and Gaussian perturbation are introduced to improve the optimization capability of the dung beetle algorithm and escape from local optima, thereby comprehensively improving the computational efficiency and accuracy.

[0075] 3. Due to the difficulty in obtaining data on the distribution characteristics of the soil and rock structural surfaces at the location of bridge pile foundations on slopes in actual engineering projects, accurate references cannot be provided for subsequent analysis of bridge pile foundations. Furthermore, to ensure safety during construction and use, designs are often overly conservative. This invention utilizes a NAR dynamic neural network structure, whose database contains a large amount of engineering geological conditions, surrounding rock grades, engineering dimensions, and surface settlement around the pile foundations in different regions. This makes the distribution patterns of non-uniform structural surfaces obtained through neural network filtering highly targeted, resulting in significant savings in engineering construction costs.

[0076] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0077] Figure 1 This is the IDBO-NAR neural network algorithm model in this embodiment of the invention;

[0078] Figure 2 This is the parameter mapping diagram after 1000 iterations of the Logistic chaotic mapping in this embodiment of the invention;

[0079] Figure 3This is a flowchart of the improved and optimized IDBO-NAR model prediction process in an embodiment of the present invention. Detailed Implementation

[0080] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0081] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0082] Example

[0083] Improved and optimized IDBO-NAR model prediction process as follows Figure 3 As shown.

[0084] The steps for constructing a numerical model for bridge pile foundations are as follows:

[0085] Step 1: Collect and organize the bridge pile foundation design database under non-uniform structural planes, including engineering geological conditions, surrounding rock grade, engineering dimensions, and surface settlement around the pile foundation in different regions;

[0086] Step 2: Classify and divide all data samples, and preprocess them. Select 75% of the samples as the training set and 25% of the samples as the test set.

[0087] Step 3: Establish the NAR dynamic neural network structure and initialize the relevant parameters of the neural network. The neural network consists of four parts: input layer, output layer, hidden layer, and lag layer, as follows: Figure 1 As shown, data y(t) enters from the input layer, then passes through the hidden layer and lag layer. After training, transmission, and learning, it reaches the output layer, thus obtaining the prediction result. Here, w is the weight, b is the threshold, 1:6 represents the delay order, and 10 represents the number of hidden layer units.

[0088] Step 4: Initialize the population using a chaotic mapping. Logistic chaotic mapping is often used to generate chaotic sequences, which are random sequences generated by simple deterministic systems. Generally, chaotic sequences exhibit nonlinearity, sensitivity to initial values, and randomness, displaying uncertainty, uniqueness, and unpredictability. It can generate uniformly distributed random number sequences and can perform non-repeating traversals of the dung beetle population state within a certain range. This increases population diversity, improves the algorithm's global search capability and convergence speed, thereby effectively improving the algorithm's solution efficiency and accuracy. The dung beetle population is initialized using a logistic chaotic mapping, including the population size, number of iterations, mutation strategy, maximum number of iterations, and adaptive weight factor. The logistic chaotic mapping can uniformly distribute the dung beetles in the search space, ultimately obtaining the optimal position and its fitness value through global search. The mathematical expression for the logistic mapping is shown in Equation (I). Figure 2 The parameter mapping diagram after 1000 iterations of the Logistic chaotic mapping;

[0089]

[0090] in, Let be the current iteration state value of the i-th variable, with a value range of [0,1]. The next iteration state value; μ is the branch parameter that determines whether the Logistic mapping is in a chaotic state, and its value ranges from [0,4].

[0091] Step 5: Calculate the initial fitness of the dung beetle population;

[0092] Step 6: Update the positions of the four types of dung beetles. The Dung Beetle Algorithm (DBO), a novel global optimization algorithm, is primarily inspired by the dung beetle's rolling, dancing, foraging, stealing, and reproductive behaviors. The DBO consists of four distinct themes: rolling dung beetles, hatching dung beetles, baby dung beetles, and thieving dung beetles, each updated according to its own rules.

[0093] (1) Rolling Dung Beetle: During the rolling process, the rolling dung beetle updates its position in two ways:

[0094] ① When there are no obstacles, it can be represented as:

[0095] x i (t+1)=x i (t)+α×k×x i (t-1)+b×△x(1)

[0096] △x=|x i (t)-X w |(2)

[0097] Where: t represents the current iteration number; x i (t) represents the position information of the i-th dung beetle in the t-th iteration; k∈(0,0.2] represents the constant of the deviation coefficient; b∈(0,1) is a constant value; α is a natural coefficient assigned the value -1 or 1; X w This indicates the worst position globally.

[0098] ② When there are obstacles: The tangent function is used to simulate the dance behavior and determine a new route. The position update definition for the dung beetle is as follows:

[0099] x i (t+1)=x i (t)+tan(θ)|x i (t)-x i (t-1)|(3)

[0100] Where: θ∈[0,π].

[0101] (2) Dung beetle: Dung beetles roll their dung balls to a safe place and hide them. Providing a safe environment for their offspring requires selecting suitable egg-laying sites. A boundary selection strategy is used to simulate the egg-laying area of ​​female dung beetles, defined as follows:

[0102] Lb * =max(X * ×(1-R),Lb)(4)

[0103] Ub * =min(X) * ×(1+R),Ub)(5)

[0104] Where: X * Lb represents the current local optimum. * and Ub * These represent the next and previous terms of the spawning region, respectively; R = 1 - t / T max and T max The maximum number of iterations is represented by Lb and Ub, which represent the next and previous iterations of the optimization problem, respectively.

[0105] The formula for updating the position of the dung beetle is as follows:

[0106] B i (t+1)=X * +b1×(B i (t)-Lb * )+b2×(B i (t)-Ub * (6)

[0107] Among them: B i(t) represents the position information of the i-th brooding ball in the nth iteration, b1 and b2 represent two independent random variables of size 1×D, and D represents the dimension of the optimization problem.

[0108] (3) Dung beetles: Dung beetles are newly grown dung beetles that forage in the best foraging area, which is defined as:

[0109] Lb b =max(X b ×(1-R),Lb)(7)

[0110] Ub b =min(X) b ×(1+R),Ub)(8)

[0111] Where: X b Lb represents the current local optimum. b and Ub b Let R represent the next and previous bounds of the optimal foraging region, respectively; R = 1 - t / T max and T max The maximum number of iterations is represented by Lb and Ub, which represent the next and previous iterations of the optimization problem, respectively.

[0112] The formula for updating the position of the dung beetle is as follows:

[0113] x i (t+1)=x i (t)+C1×(x i (t)-Lb b )+C2×(x i (t)-Ub b (9)

[0114] Where: x i (t) represents the position information of the i-th dung beetle in the nth iteration, C1 represents a random number that follows a normal distribution, and C2 represents a random vector belonging to (0,1).

[0115] (4) The thieving dung beetle: It steals dung balls from other dung beetles. Assume X... b The surrounding area represents the best location for competing for food. During the iteration process, the dung beetle's location information is updated as follows:

[0116] x i (t+1)=X b +S×g×(|x i (t)-X * |+|x i (t)-X b |)(10)

[0117] Where: x i(t) represents the location information of the i-th thief in the nth iteration, g is a random vector of size 1×D that follows a normal distribution, and S represents a constant.

[0118] Step 7: Action Mutation Strategy. To enable each dung beetle to perform four actions, a time-varying approach is proposed, using iterations to simulate the changes in time. Every M iterations, action mutation is performed, changing the current action to the next action strategy. Population diversity is represented as follows:

[0119]

[0120] in: This represents the optimal value in both the local and global optimal solutions; the rest have the same meaning as above.

[0121] When Diver > 0.5, the population diversity is too low, which may lead to getting stuck in local optima. The number of dung beetles and small dung beetles determines the algorithm's ability to explore the solution space and its convergence speed. Therefore, individuals performing the hatching dung beetle and small dung beetle actions are mutated to individuals performing the rolling dung beetle actions to enhance the algorithm's global search ability and increase species diversity. After finding a new optimal individual or reaching the iteration threshold Tmax for mutated individuals, the mutated individuals are restored to their original behavior and the search continues.

[0122] Step 8: Introduce adaptive weights for iterative position updates of the dung beetle. During the foraging phase of the dung beetle algorithm, the foraging behavior of the dung beetle has a significant impact on the algorithm's performance. Traditional formulas for dung beetle foraging behavior typically only consider searches in two directions, lacking global search capability and diversity. To increase the global search capability and diversity of the dung beetle, we borrow the iterative optimization spiral-upward search method from the whale optimization algorithm and introduce adaptive weight factors. The specific position update method is as follows:

[0123]

[0124] Where: X i (t+1) represents the updated position of the i-th dung beetle, X best (t) represents the optimal position in the t-th iteration, γ is a uniformly random number in (0,1], and iter max This represents the maximum number of iterations for the population.

[0125] Step 9: Update the spatial position of the dung beetle according to formula (13). Randomly perturb the dung beetle in the optimal position. The position update function is:

[0126]

[0127] In the formula: X i (t+1) represents dung beetle X iThe position after the (t+1)th move, X i (t) represents dung beetle X i The position after the t-th move, X j (t) represents dung beetle X j The position after the t-th move, ζ represents the step size factor which is a constant in the range [0,1], and rand is a random factor that follows a uniform distribution in the range [0,1].

[0128] Step 10: To improve the algorithm's optimization ability and escape local optima, Gaussian mutation and Gaussian perturbation are introduced. Gaussian mutation refers to changing the mean μ, σ... 2 A random number is drawn from a normal distribution and used to replace the parameter variables in the dung beetle algorithm to achieve the goal of optimizing the algorithm. Gaussian perturbation is used to improve the ability to escape local optima. After each iteration, a small Gaussian perturbation is applied to the optimal position of the individual dung beetle to help it better escape the local optimum.

[0129] The fitness value F of the population is expressed as shown in equation (14), where f(X) is the fitness function:

[0130] F=[f(X1)f(X2)…f(X n )] T (14)

[0131] In the formula: X i Let f(X) be the position of the i-th dung beetle. i ) represents the fitness value of an individual dung beetle;

[0132] When f i (Current fitness value of the individual) <f av (Average fitness value) The optimal individual of the population is determined by introducing Gaussian mutation (15), when f i ≥f av By introducing Gaussian perturbation equations (16) and (17) to determine the optimal individuals in the population, the convergence speed and evolutionary performance of FA can be accelerated by combining Gaussian mutation and Logistic chaotic mapping.

[0133] T g =Lo(1+N(0,1))(15)

[0134] In the formula: N(0,1) is a normally distributed random number with an expected value of 0 and a standard deviation of 1; T g The value is calculated by Gaussian mutation after initializing the parameters;

[0135] G b =G(1+Gaussian(μ,σ) 2 ))(16)

[0136]

[0137] Where: G b Let G be the optimal position of the dung beetle in each iteration; G is the fitness of the dung beetle before Gaussian perturbation, Gaussian(μ,σ) 2 The mean is μ and the variance is σ. 2 Gaussian function; To determine the optimal fitness of the disturbed dung beetle individual; G t Let be the optimal fitness of the dung beetle individual in the t-th iteration;

[0138] Step 11: Obtain the current updated optimal population position. If the new position is better than the old position in the previous iteration, perform the update operation; otherwise, return to step 3 and continue the iteration operation until the condition is met.

[0139] Step 12: Output the optimal delay order and number of hidden layers, and feed them back to the NAR dynamic neural network for retraining, testing, prediction, and output of results.

[0140] This invention utilizes a collected and organized database of bridge pile foundation design under non-uniform structural planes, including engineering geological conditions, surrounding rock grades, engineering dimensions, and surface settlement around the pile foundations in different regions, to establish a NAR dynamic neural network structure. A Logistic chaotic mapping is used to initialize the dung beetle population. By determining the corresponding parameters of the dung beetle population, the spatial location of the dung beetles is iteratively obtained, thus determining the distribution of the structural plane. Gaussian mutation and Gaussian perturbation are introduced to improve the optimization capability of the dung beetle algorithm and help it escape local optima, obtaining the currently updated optimal population position. This invention combines the NAR dynamic neural network structure, the chaotic mapping-initialized population, and the dung beetle algorithm to ultimately determine the numerical calculation model for non-uniform structural plane pile foundations that best fits the bridge pile foundation design database. This model possesses regionality, accuracy, efficiency, and economy, thereby avoiding the repetitiveness of human-designed solutions, the complexity of multi-factor influences, and the accuracy of human-influenced schemes, effectively ensuring the safety of relevant personnel and property, and improving resource utilization.

[0141] Therefore, this invention adopts the above-mentioned method for constructing a numerical model of bridge pile foundation with unevenly distributed structural surfaces. It combines the NAR dynamic neural network structure, the chaotic mapping initialization population and the dung beetle algorithm to finally determine the calculation model that best fits the bridge pile foundation design database under uneven structural surfaces. This calculation model has high accuracy and efficiency, while saving economic costs.

[0142] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. 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 still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for constructing a numerical model of bridge pile foundations with unevenly distributed structural surfaces, characterized in that, Includes the following steps: Step 1: Collect and organize the bridge pile foundation design database under non-uniform structural planes, including engineering geological conditions, surrounding rock grade, engineering dimensions, and ground settlement around the pile foundation in different regions; Step 2: Classify and preprocess all data samples, and select 75% of the samples as the training set and 25% of the samples as the test set. Step 3: Establish the NAR dynamic neural network structure and initialize the relevant parameters of the neural network; the neural network includes an input layer, an output layer, a hidden layer, and a lag layer. Data enters from the input layer, enters the hidden layer and the lag layer, and after training, transmission, and learning, it reaches the output layer to obtain the prediction result; Step 4: Initialize the population using chaotic mapping. The dung beetle population is initialized using Logistic chaotic mapping. Step 5: Calculate the initial fitness of the dung beetle population; Step 6: Update the locations of the four types of dung beetles, including the rolling dung beetle, the hatching dung beetle, the small dung beetle, and the thieving dung beetle, updating them according to their respective rules; Step 7: Action Mutation Strategy; In order for each dung beetle to perform 4 actions, the time change is simulated by the number of iterations, and action mutation is performed once every M iterations; Step 8: Introduce adaptive weights to iteratively update the position of the dung beetle; adopt the spiral ascending search method of iterative optimization in the whale optimization algorithm to increase the global search capability and diversity of the dung beetle, and introduce adaptive weight factors; Step 9: Update the spatial location of dung beetles by randomly disturbing those in the best positions; Step 10: To improve the algorithm's optimization capability and escape local optima, Gaussian mutation and Gaussian perturbation are introduced; Step 11: Obtain the current updated optimal population position. If the new position is better than the old position in the previous iteration, perform the update operation; otherwise, return to step 3 and continue the iteration operation until the condition is met. Step 12: Output the optimal delay order and number of hidden layers, and feed them back to the NAR dynamic neural network for retraining, testing, prediction, and output of results.

2. The method for constructing a numerical model of bridge pile foundations with unevenly distributed structural surfaces according to claim 1, characterized in that: In step 4, the dung beetle population is initialized using a Logistic chaotic mapping, including the population size, number of iterations, mutation strategy, maximum number of iterations, and adaptive weight factor. The Logistic chaotic mapping can uniformly distribute the dung beetles in the search space, and finally, the optimal position and its fitness value are obtained through global search. The mathematical expression of the Logistic mapping is shown in equation (I). （Ⅰ） in, For the first The current iterative state value of each variable, with a value range of [0,1]; This is the state value for the next iteration; The branch parameter determines whether the Logistic mapping is in a chaotic state, and its value ranges from [0,4].

3. The method for constructing a numerical model of bridge pile foundations with unevenly distributed structural surfaces according to claim 1, characterized in that, The update rule for the dung beetle in step 6 is as follows: During the rolling process, the dung beetle's position update occurs in two ways: ① When there are no obstacles, it can be represented as: （1） （2） Where: t represents the current iteration number; This represents the position information of the i-th dung beetle at the t-th iteration; A constant representing the deviation coefficient; A constant value; It is a natural coefficient that is assigned the value -1 or 1; Indicates the worst position globally; ② When there are obstacles: The tangent function is used to simulate the dance behavior to determine a new route. The position update definition for the dung beetle is as follows: （3） in: .

4. The method for constructing a numerical model of bridge pile foundations with unevenly distributed structural surfaces according to claim 1, characterized in that, The update rule for the dung beetle in step 6 is as follows: Dung beetles roll their dung balls to a safe place and hide them, providing a safe environment for their offspring. Choosing a suitable egg-laying site is crucial. A boundary selection strategy is used to simulate the egg-laying area of ​​female dung beetles, defined as follows: （4） （5） in: This indicates the current local optimum. and These respectively represent the next and previous generations of the spawning area; , This represents the maximum number of iterations, and Lb and Ub represent the next and previous iterations of the optimization problem, respectively. The formula for updating the position of the dung beetle is as follows: （6） in: Let b1 and b2 represent the position information of the i-th brooding ball in the nth iteration, and let D represent two independent random variables of size 1×D, where D represents the dimension of the optimization problem.

5. The method for constructing a numerical model of bridge pile foundations with non-uniformly distributed structural surfaces according to claim 1, characterized in that, The update rule for the dung beetle in step 6 is as follows: Dung beetles are newly grown dung beetles foraging in their optimal foraging area, which is defined as: （7） （8） in: This indicates the current local optimum. and These represent the next and previous iterations of the optimal foraging region, respectively. , This represents the maximum number of iterations, and Lb and Ub represent the next and previous iterations of the optimization problem, respectively. The formula for updating the position of the dung beetle is as follows: （9） in: Let C1 represent the position information of the i-th dung beetle in the nth iteration, C2 represent a random number that follows a normal distribution, and C3 represent a random vector belonging to (0,1).

6. The method for constructing a numerical model of bridge pile foundations with unevenly distributed structural surfaces according to claim 1, characterized in that, The update rule for the dung beetle in step 6 is as follows: The thieving dung beetle will steal dung balls from other dung beetles, assuming... The surrounding area represents the best location for competing for food. During the iteration process, the dung beetle's location information is updated as follows: （10） in: Let g represent the location information of the i-th thief in the nth iteration, g is a random vector of size 1×D that follows a normal distribution, and S represents a constant. This indicates the current local optimal position.

7. The method for constructing a numerical model of bridge pile foundations with non-uniformly distributed structural surfaces according to claim 1, characterized in that, In step 7, to ensure that each dung beetle can perform four actions, the number of iterations is used to simulate time changes. Every M iterations, an action mutation is performed, changing the current action to the behavior strategy for the next chapter. The population diversity is represented as follows: （11） in: This represents the optimal value among the local and global optimal solutions.

8. The method for constructing a numerical model of bridge pile foundations with unevenly distributed structural surfaces according to claim 1, characterized in that, The specific location update method in step 8 is as follows: （12） in: Let i be the updated position of the i-th dung beetle. This represents the optimal position in the t-th iteration. A uniformly random number in (0,1] This represents the maximum number of iterations for the population.

9. The method for constructing a numerical model of bridge pile foundations with non-uniformly distributed structural surfaces according to claim 1, characterized in that, The position update function in step 9 is: （13） in: Dung beetle The position after the (t+1)th move. Dung beetle Position after the t-th move Dung beetle Position after the t-th move The step size factor is a constant in the range [0,1], and rand is a random factor that follows a uniform distribution in the range [0,1].

10. The method for constructing a numerical model of bridge pile foundations with non-uniformly distributed structural surfaces according to claim 1, characterized in that: In step 10, Gaussian variation refers to the process of transforming the mean... A random number is drawn from the normal distribution and used to replace the parameter variables in the dung beetle algorithm to achieve the purpose of optimizing the algorithm; Gaussian perturbation is used to improve the ability to escape local optima. A small Gaussian perturbation is applied to the optimal position of the individual dung beetle after each iteration to help it escape the local optimum better. The fitness value F of the population is expressed as shown in equation (14), where For the fitness function: （14） In the formula: For the first The location of the dung beetle. This represents the fitness value of an individual dung beetle. when The optimal individual of the population is determined by introducing Gaussian mutation formula (15), when By introducing Gaussian perturbation equations (16) and (17) to determine the optimal individuals of the population, the convergence speed and evolutionary performance of FA can be accelerated by combining Gaussian mutation and Logistic chaotic mapping. （15） In the formula: These are normally distributed random numbers with an expected value of 0 and a standard deviation of 1. The value is calculated by Gaussian mutation after initializing the parameters; （16） （17） In the formula: This represents the optimal position of the dung beetle in each iteration; The fitness of the dung beetle before Gaussian perturbation. The mean is variance is Gaussian function; To determine the optimal fitness of the disturbed dung beetle individuals; Let be the optimal fitness of the dung beetle individual in the t-th iteration.

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