A soft rock tunnel large deformation prediction method based on particle swarm optimization neural network

Abstract

The application relates to the technical field of tunnel engineering disaster prediction, and discloses a soft rock tunnel large deformation prediction method based on a particle swarm optimization neural network, which comprises the following steps: selecting geological construction characteristic parameters such as water content of surrounding rock and construction methods as input factors, and establishing a qualitative index and quantitative value mapping; based on orthogonal test design and numerical simulation, engineering sample data sets are constructed and normalized; subsequently, the initial connection weight and bias of an error back propagation neural network are globally iteratively optimized by using a particle swarm optimization algorithm, so that optimal initial values are obtained by taking network errors as fitness values; finally, data training is carried out to generate a mature model, and a predicted deformation value is output and combined with a double check mechanism to carry out engineering early warning. The application solves the problems that traditional neural networks are slow in convergence and prone to falling into local optimization due to random parameter initialization, and effectively improves the prediction accuracy of soft rock tunnel large deformation and the reliability of engineering early warning.

Description

Technical Field

[0001] This invention relates to the field of tunnel engineering disaster prediction technology, specifically a method for predicting large deformations in soft rock tunnels based on particle swarm optimization neural networks. Background Technology

[0002] Soft rock tunnels are highly susceptible to large deformation disasters during construction, severely impacting project safety and progress. To effectively predict the deformation trend of the surrounding rock, the engineering community has introduced artificial intelligence algorithms such as neural networks to construct nonlinear prediction models. However, the widely used backpropagation (BP) neural network still has significant technical limitations in practical applications.

[0003] First, traditional backpropagation neural network algorithms primarily adjust network parameters based on the gradient descent principle, making their training process highly sensitive to the initial connection weights and biases. Existing techniques typically initialize these parameters randomly, which makes the network training process prone to getting trapped in local minima rather than the global optimum. This results in slow convergence, low training efficiency, and insufficient prediction accuracy when dealing with highly nonlinear problems such as large deformations in soft rock.

[0004] Secondly, the predictive performance of neural network models heavily depends on the quality and breadth of training samples. In actual engineering, factors causing large deformations in soft rock tunnels include both continuous geological parameters such as surrounding rock water content and in-situ stress, and discrete qualitative parameters such as construction methods and support levels. Existing technologies often struggle to effectively handle these qualitative factors through quantitative methods when constructing datasets, and primarily rely on field measurement data. Because large deformation accidents are low-probability, high-risk events, high-risk sample data from field measurements are extremely scarce, leading to an uneven distribution of training samples under different working conditions. This results in poor generalization ability of the trained models, making it difficult to adapt to complex and ever-changing engineering sites.

[0005] Furthermore, in terms of engineering early warning based on prediction results, existing early warning systems typically employ a single threshold judgment mode, which simply compares the predicted or monitored values ​​with the design allowable values. This approach lacks dynamic analysis of the deformation evolution trend of the surrounding rock and multi-dimensional cross-validation, making it unable to effectively distinguish between measurement errors and actual risks. It is prone to false alarms or missed judgments in practical applications, making it difficult to accurately guide the timely adjustment of support parameters during construction, and failing to meet the stringent requirements for the reliability of safety early warnings in high-risk soft rock tunnels. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for predicting large deformations in soft rock tunnels based on particle swarm optimization neural networks. This method solves the problem that in traditional large deformation prediction of soft rock tunnels, the error backpropagation neural network suffers from slow convergence speed and is prone to getting trapped in local minima due to the random selection of initial values ​​for connection weights and biases. As a result, the prediction accuracy is low and it cannot meet the requirements for engineering safety early warning.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for predicting large deformation of soft rock tunnels based on particle swarm optimization neural networks is proposed. The prediction method combines the global search capability of particle swarm optimization algorithm with the local precise optimization capability of error backpropagation algorithm. The completeness of sample data is ensured by orthogonal experimental design, and the method realizes quantitative prediction and graded early warning of the deformation of the surrounding rock of soft rock tunnels.

[0009] The specific technical solution adopted in this invention is as follows:

[0010] S1: Determine the input factors that affect the large deformation of soft rock tunnels. The input factors specifically include geological construction characteristic parameters, and set the geological construction characteristic parameters as input layer variables of the neural network.

[0011] Preferably, in specific implementation, the selected geological construction characteristic parameters include the surrounding rock moisture content, tunnel construction method, tunnel support conditions, tunnel burial depth, surrounding rock dip angle, surrounding rock layer thickness, and lateral pressure coefficient. For the tunnel construction method and tunnel support conditions, which are non-continuous qualitative variables, a mapping relationship between qualitative indicators and quantitative integer values ​​is established in advance so that they can be recognized and processed by the neural network.

[0012] S2: Obtain engineering sample data containing the input factors and the corresponding large deformation convergence values ​​of the surrounding rock, and normalize the engineering sample data using the minimum-maximum normalization algorithm to form a standardized neural network input matrix.

[0013] Preferably, to ensure the representativeness and completeness of the sample data, the process of establishing engineering sample data is based on the principle of orthogonal experimental design. Orthogonal combined working conditions are constructed by selecting typical level values ​​of various input factors, and numerical simulation software is used to simulate and calculate each group of orthogonal combined working conditions. The maximum deformation convergence value under each working condition is extracted, thereby constructing a sample dataset containing the input factors and the convergence value of the large deformation of the surrounding rock. In the data preprocessing stage, the maximum and minimum values ​​of each type of input factor in the dataset are calculated. The data is normalized by using the ratio of the difference between the current sample value and the minimum value to the range, thus eliminating the influence of dimensional differences on network training.

[0014] S3: Construct an initial model of the backpropagation neural network for error, and use the particle swarm optimization algorithm to perform global iterative optimization on the connection weights and biases of the initial model. Set the network prediction error as the fitness value, search for the global optimal position vector and parse it into the optimal initial connection weights and optimal initial biases, and complete the construction of the particle swarm optimization neural network model.

[0015] Preferably, the initial model of the error backpropagation neural network is constructed as a three-layer structure, wherein the number of nodes in the input layer and the output layer corresponds to the number of input factors and the number of convergent values ​​of large deformation of the surrounding rock, respectively, and the number of nodes in the hidden layer is determined by an empirical formula. The inter-layer transfer functions are respectively set as a logarithmic sigmoid transfer function and a linear transfer function.

[0016] Preferably, in the particle swarm optimization process, to encode the neural network parameters, the connection weight matrix from the input layer to the hidden layer, the bias vectors of each node in the hidden layer, the connection weight matrix from the hidden layer to the output layer, and the bias vectors of the output layer nodes are sequentially concatenated to form a high-dimensional real vector as the particle's position vector. By initializing the positions and velocities of particles in the swarm, using the network prediction error as the fitness evaluation criterion, and employing a linear decreasing strategy to control the inertia weights, individual learning factors, and social learning factors, the particle state is dynamically updated until the iteration termination condition is met, thereby searching for a set of globally optimal initial weights and biases in the solution space.

[0017] S4: Input the normalized engineering sample data into the particle swarm optimization neural network model for error backpropagation training to generate a mature prediction model for large deformation of soft rock tunnels. Input the normalized geological construction data to be predicted into the mature prediction model for large deformation of soft rock tunnels, output the deformation prediction results and provide engineering early warning.

[0018] Preferably, the training process starts with the optimal initial connection weights and optimal initial biases obtained in step S3, calculates the forward propagation error, and corrects the parameters in reverse according to the gradient descent principle until the mean square error meets the preset threshold. In the model output stage, inverse normalization is performed to restore the normalized predicted values ​​of the model output to the final deformation predicted values ​​with physical length units. The final engineering early warning adopts a dual verification mechanism, that is, simultaneously comparing the final deformation predicted value with the tunnel design allowance deformation amount, and comparing it with the limit value of the evolution curve fitted to the field monitoring data. A large deformation graded early warning signal is issued only when both show that the deformation exceeds the standard, in order to reduce the false alarm rate.

[0019] This invention provides a method for predicting large deformations in soft rock tunnels based on particle swarm optimization neural networks.

[0020] It has the following beneficial effects:

[0021] 1. This invention overcomes the shortcomings of traditional neural networks, such as being prone to getting trapped in local minima and having slow convergence speed due to random parameter initialization, by using the particle swarm optimization algorithm to perform global iterative optimization of the initial connection weights and biases before training the error backpropagation neural network, and using the network prediction error as the fitness value to search for the globally optimal initial parameters. This effectively improves the nonlinear mapping capability and prediction accuracy of the large deformation prediction model for soft rock tunnels.

[0022] 2. This invention establishes a qualitative index and quantitative numerical mapping relationship between tunnel construction methods and support conditions, and constructs a combination of working conditions containing multiple geological construction characteristic parameters based on the orthogonal experimental design principle for numerical simulation. This solves the problem of difficulty in obtaining high-risk samples of large deformation measured on-site, and ensures the balance and representativeness of neural network training samples at the input factor level, thereby improving the model's generalization ability to different complex working conditions.

[0023] 3. This invention employs a dual verification mechanism for engineering early warning, which simultaneously compares the model's predicted values ​​with the design's reserved deformation amount and the limit values ​​of the evolution curve of the field monitoring data. It comprehensively determines the risk level by combining the design standards with the actual deformation trend, avoiding misjudgments or omissions caused by a single basis, and providing timely and reliable decision-making basis for adjusting support parameters during the construction period of soft rock tunnels. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating the overall process of predicting large deformations in soft rock tunnels based on particle swarm optimization neural networks, according to an embodiment of the present invention.

[0025] Figure 2 This is a schematic diagram of the data feature parameter quantization and normalization preprocessing flow according to an embodiment of the present invention;

[0026] Figure 3 This is a schematic diagram of the PSO-BP neural network topology according to an embodiment of the present invention;

[0027] Figure 4 This is a flowchart illustrating the initial weights and thresholds of the particle swarm optimization neural network according to an embodiment of the present invention.

[0028] Figure 5 This is a flowchart of the joint training process of the BP neural network based on PSO optimization according to an embodiment of the present invention;

[0029] Figure 6 This is a schematic diagram illustrating the model prediction performance evaluation and engineering application process of an embodiment of the present invention. Detailed Implementation

[0030] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] See attached document Figure 1 This invention provides a method for predicting large deformation of soft rock tunnels based on particle swarm optimization neural networks, which includes orthogonal data experiment and acquisition, data normalization preprocessing, neural network topology construction, particle swarm parameter optimization, error backpropagation training, and engineering application prediction steps.

[0032] In this embodiment, based on the geological environment and construction conditions of soft rock tunnel engineering, seven key characteristic parameters affecting the convergence value of large deformation of the tunnel surrounding rock are first determined: tunnel depth, support conditions, construction method, water content of surrounding rock, dip angle of surrounding rock, thickness of surrounding rock layer, and lateral pressure coefficient. To ensure that the training samples can evenly cover various working condition combinations and are representative, this embodiment uses orthogonal experimental design method to set multiple sets of numerical simulation working conditions. Considering that the large deformation of the tunnel surrounding rock is affected by multiple coupled factors, if a comprehensive experimental method is used, the number of experiments will increase exponentially. Therefore, based on the orthogonal design principle, typical level values ​​of each characteristic parameter (such as different water content gradients, different burial depth levels, etc.) are selected to construct representative orthogonal combination working conditions. Numerical calculation software (such as FLAC3D, etc.) is used to simulate and calculate each set of orthogonal working conditions, and the maximum convergence value of large deformation of the tunnel surrounding rock under each working condition is extracted. This method not only effectively reduces the computational load of numerical simulation, but also ensures the uniform distribution of the sample space across all factor levels, thereby constructing a high-quality sample dataset containing the seven input feature parameters and one output deformation parameter.

[0033] The water content of the surrounding rock mainly reflects the softening characteristic of soft rock when exposed to water. High water content leads to an exponential decrease in the strength of soft rock, which is an intrinsic factor inducing large deformations. The lateral pressure coefficient and tunnel depth jointly determine the initial geostress field state of the surrounding rock, especially high-level tectonic stress, which is the main driving force for asymmetric large deformations of the tunnel. The dip angle and thickness of the surrounding rock determine the anisotropic characteristics and potential sliding failure modes of the surrounding rock. Construction methods and support conditions are controllable engineering variables that directly affect the stress release rate and redistribution process of the surrounding rock. By coupling these seven parameters into a neural network, the nonlinear feedback relationship between geology, stress, and support can be comprehensively mapped.

[0034] For the constructed sample dataset, Min-Max regularization is performed. Since each feature parameter has different dimensions and physical units, directly inputting it into the network will lead to numerical computation instability. Therefore, the maximum and minimum values ​​of each feature parameter in the entire dataset are calculated, and all sample data are mapped to the numerical range [0, 1] to form a standardized neural network input matrix.

[0035] A backpropagation (BP) neural network topology suitable for predicting large deformations in soft rock was constructed. The network was set to a three-layer structure, with seven neurons in the input layer corresponding to the seven feature parameters, and one neuron in the output layer outputting the predicted deformation convergence value. The number of nodes in the hidden layer was determined to be five based on the number of nodes in the input and output layers and the training sample size, through empirical formulas and trial calculations. The hidden layers employed a log-sigmoid transfer function to handle nonlinear mappings, while the output layer used a purelin transfer function to output real values.

[0036] Before network training, a particle swarm optimization (PSO) algorithm is introduced to globally optimize the initial connection weights and thresholds of the backpropagation (BP) neural network. The connection weight matrices from the input layer to the hidden layers, the bias vectors of each node in the hidden layers, the connection weight matrices from the hidden layers to the output layer, and the bias vectors of the output layer nodes in the BP neural network are expanded and concatenated to form a position vector in the particle swarm. The dimension of this position vector is equal to the total number of all weights and biases in the network. The training data is input into the neural network with the corresponding parameters, and the mean squared error between the network output value and the true value is calculated. This mean squared error is used as the fitness function value to evaluate the quality of the particle positions. By iteratively updating the particle velocity and position, the global optimal position that minimizes the fitness function value is searched, and this position is analytically converted into the optimal initial weights and biases of the neural network.

[0037] The BP neural network is initialized using the obtained optimal initial parameters, and backpropagation training is performed based on the training set. The predicted output is calculated during forward propagation, and the weights and biases of each layer are adjusted according to the gradient direction of the prediction error during backpropagation until the network training error converges to the preset accuracy or reaches the maximum number of training iterations, thus obtaining a mature prediction model for large deformation of soft rock tunnels.

[0038] In the engineering application phase, the actual geological and construction parameters of the tunnel to be predicted are normalized according to the same standard and then input into the prediction model, outputting the predicted convergence value of the large deformation of the tunnel surrounding rock. Further, this predicted convergence value is compared with the tunnel's designed safety limit deformation value, or an evolution curve is fitted using time-series data measured on-site. When the predicted value or evolution trend exceeds a preset safety threshold, a large deformation early warning mechanism is triggered, guiding on-site adjustments to support parameters or construction methods.

[0039] The first step is to obtain the seven-dimensional geological construction parameters of the section to be excavated in front of the current tunnel face (especially the water content and in-situ stress parameters of the surrounding rock of carbonaceous slate sandstone), input them into the trained PSO-BP model, and output the predicted final deformation convergence value Y. predict .

[0040] The second step involves using real-time deformation time-series data from on-site monitoring to fit the deformation evolution curve of the surrounding rock using a nonlinear regression method.

[0041] The third step is to use the Y predicted by the PSO-BP model. predict The deformation value is compared with the ultimate deformation value calculated by the evolution equation. If both indicate that the deformation will exceed the tunnel design allowance or the safety specification allowable value (e.g., the daily deformation rate continuously exceeds the warning threshold), it is determined that there is an extremely high risk of large deformation encroachment. A graded warning signal will be immediately triggered to guide the construction party to take timely control measures such as increasing the initial support stiffness, implementing advanced support, or adjusting to the short-step construction method. This achieves closed-loop management of soft rock tunnel construction safety based on a combination of data-driven and on-site measurement.

[0042] See attached document Figure 2 After completing the data acquisition and experimental design steps in the overall process, the input variables that affect the large deformation of soft rock tunnels are specifically quantified and preprocessed.

[0043] This embodiment selects seven physical, mechanical, and construction parameters that are significantly correlated with the deformation of the surrounding rock in carbonaceous slate sandstone tunnels as input layer variables for the neural network. These seven parameters specifically include: surrounding rock water content, tunnel construction method, tunnel support conditions, tunnel depth, surrounding rock dip angle, surrounding rock layer thickness, and lateral pressure coefficient. Among these, the surrounding rock water content reflects changes in the physical and mechanical properties of soft rock; soft rock experiences a decrease in strength and expansion deformation after encountering water. Tunnel depth and lateral pressure coefficient define the initial geostress state of the tunnel site. The surrounding rock dip angle and surrounding rock layer thickness reflect the structural characteristics of the surrounding rock and influence its failure mode. Construction method and support conditions, as human-controlled factors, impose constraints on the deformation of the surrounding rock.

[0044] To address the aforementioned influencing factors, since construction methods and support conditions are discontinuous qualitative variables, this embodiment establishes a mapping relationship between qualitative indicators and quantitative values ​​based on the degree of disturbance to the surrounding rock caused by each construction method and the constraint stiffness of the surrounding rock by each support type. This allows the qualitative indicators to be recognized by the neural network and participate in numerical calculations. Specifically, for construction method X3, different excavation methods such as the full-section method and the bench method not only cause different disturbance ranges to the surrounding rock, but also assign corresponding integer values ​​for disturbance levels. For support condition X2, a support strength level system is established based on different combinations of shotcrete thickness, steel frame type, and spacing, and quantifies it into a continuous integer sequence representing the strength of the support (e.g., level values ​​from 1 to 4). Combined with the remaining five continuous quantitative parameters (tunnel depth X1, surrounding rock moisture content X4, surrounding rock dip angle X5, surrounding rock layer thickness X6, and lateral pressure coefficient X7), a seven-dimensional data sample is formed. To ensure that the sample space can cover various possible engineering conditions, a tunnel excavation model with different orthogonal combinations of parameters is established using numerical simulation software. The maximum deformation Y corresponding to each model is calculated and extracted, thereby generating the input and output datasets for neural network training.

[0045] After obtaining the original dataset, the seven input feature parameters have different physical dimensions. For example, the tunnel burial depth may be between 300 and 600, while the lateral pressure coefficient is usually between 1.3 and 1.4. This difference in numerical scale can cause large numerical features to dominate the weight update direction during gradient descent, resulting in slow network convergence or getting trapped in local extrema. To eliminate the difference in data dimensions, this embodiment uses the Min-Max regularization method to uniformly map all data in the input layer to the standard interval [0, 1]. The calculation formula for Min-Max regularization is expressed as:

[0046]

[0047] Where: x normalize represents the dimensionless value after normalization, which is directly used as the input signal for the corresponding node in the neural network input layer; x represents the unprocessed feature parameter value in the original dataset; x min This represents the minimum value of the feature parameter across the entire training sample space; x max This represents the maximum value of the feature parameter across the entire training sample space.

[0048] The above formula transforms all input data across all dimensions to the same order of magnitude, preserving the original data's distribution pattern while simultaneously satisfying the input sensitivity range requirements of the subsequent Log-Sigmoid activation function in the neural network. Only after standardizing all samples is the dataset divided into training and test sets before being fed into the prediction model for learning.

[0049] See attached document Figure 3 After completing data collection and Min-Max normalization preprocessing, a multi-layer feedforward neural network model based on the error backpropagation algorithm is constructed to map the nonlinear relationship between geological construction parameters and surrounding rock deformation.

[0050] Based on the engineering characteristics of the carbonaceous slate sandstone in the Litang Tunnel, this embodiment designs a three-layer network structure: an input layer, a hidden layer, and an output layer, with full connectivity between each layer. The number of neurons in the input layer is determined by the number of key factors affecting the deformation of the surrounding rock, corresponding to the determined water content of the surrounding rock, construction method, support conditions, tunnel depth, rock dip angle, rock layer thickness, and lateral pressure coefficient. Therefore, the number of nodes m in the input layer is set to 7. The output layer is used to output the predicted convergence value of the large deformation of the surrounding rock; therefore, the number of nodes n in the output layer is set to 1.

[0051] The choice of the number of hidden layer nodes determines the complexity and fitting accuracy of the network. To avoid underfitting due to too few nodes or overfitting and excessive training time due to too many nodes, this embodiment uses an empirical formula combined with a trial-and-error method to determine the optimal number of hidden layer nodes. The approximate range of the number of nodes is defined based on the following empirical formula:

[0052]

[0053] Where: p represents the number of neurons in the hidden layer; m represents the number of neurons in the input layer (m=7); n represents the number of neurons in the output layer (n=1); c represents the adjustment constant, which is an integer between [1, 10].

[0054] Based on the above formula, the value range of the number of hidden layer nodes p is approximately [4, 13]. Within this range, through repeated training and trial calculations on a sample set constructed based on field monitoring data, and comparing the mean square error of the network under different numbers of nodes, it was finally determined that when the number of hidden layer nodes p = 5, the network has the smallest prediction error and the best convergence stability. Therefore, the neural network topology structure of this embodiment is determined to be a 7-5-1 structure.

[0055] After determining the topology, the signal transfer functions of each layer of the network are defined. The hidden layer is responsible for mapping samples from the input space to the hidden space. In order to handle the complex nonlinear characteristics of the deformation factors of carbonaceous slate sandstone, the log-sigmoid function is selected as the transfer function of the hidden layer. This function maps the input signals of the hidden layer neurons to the interval (0, 1) to capture the nonlinear characteristics between data.

[0056] The output layer receives the output signal from the hidden layer and performs linear weighting. In order to achieve real-valued prediction of the deformation (covering the entire nonlinear interval after normalization), the output layer transfer function is a linear function (Purelin), and the weighted sum of the neurons is directly output as the predicted value.

[0057] To evaluate the performance of the constructed neural network during training, an error function is defined for the network. This embodiment uses mean squared error (MSE) as the evaluation metric to guide the subsequent fitness calculation in the particle swarm optimization algorithm and the gradient descent direction in the backpropagation algorithm. The error function is defined as follows:

[0058]

[0059] Among them: E k This represents the prediction error energy of the network under the current sample; n represents the number of neurons in the output layer (n=1); y represents the actual predicted output value of the output layer of the neural network; k This represents the true expected output value (i.e., the normalized value of the actual monitored deformation) in the training samples.

[0060] In summary, this BP neural network, through a defined topology (7, 5, 1) and a specific combination of transfer functions, establishes a mathematical mapping model from seven-dimensional geological construction parameters to one-dimensional deformation, providing a foundation for the subsequent introduction of the particle swarm optimization (PSO) algorithm to globally optimize the initial weights and biases of the network.

[0061] See attached document Figure 4 After determining the BP neural network with a 7, 5, 1 topology, this embodiment uses the particle swarm optimization (PSO) algorithm to globally optimize the initial connection weights and thresholds of the neural network, taking into account the characteristics of traditional gradient descent method being sensitive to initial parameters and prone to getting trapped in local extrema.

[0062] This embodiment first establishes a mapping mechanism between particle swarm optimization and neural network parameters. Each particle in the particle swarm represents a potential solution in the solution space of the neural network parameters; that is, a single particle contains all the weights and biases required by a complete backpropagation (BP) neural network. Based on the aforementioned network structure with 7 input layer nodes, p = 5 hidden layer nodes, and n = 1 output layer nodes, the total dimension D of the particles is determined by the number of connection weights from the input layer to the hidden layer, the number of biases for each node in the hidden layer, the number of connection weights from the hidden layer to the output layer, and the number of biases for each node in the output layer. The specific calculation logic is as follows:

[0063] D=m×p+p+p×n+n=7×5+5+5×1+1=46;

[0064] Therefore, the position vector x of each particle ii Given a 46-dimensional real vector, the elements of this vector correspond sequentially to w in the network. 11 …w 75 The input layer and hidden layer weights, the hidden layer biases of b1…b5, and w′ 11 …w′ 51 The hidden layer and output layer weights and the output layer bias of b′1.

[0065] After determining the encoding mechanism, initialize the particle swarm parameters. Set the population size (e.g., 20 to 50 particles) and randomly initialize the position vector x of each particle. i and velocity v i Considering that the input data has been normalized (e.g. to the range of [0, 1]), the range of particle position vector values ​​is restricted to an interval that matches the normalized values ​​(e.g., [-1, 1] or [0, 1]) to ensure the rationality of the initial parameters.

[0066] To evaluate the quality of each particle, a fitness function is defined. This embodiment directly uses the mean squared error (MSE) of the neural network on the training set as the fitness value. Specifically, the position vector of the i-th particle is decoded and assigned to the corresponding weights and thresholds of the BP neural network. Forward propagation is performed using the training set data, and the resulting prediction error is the fitness value of that particle. The smaller the fitness value, the better the initial parameter combination represented by that particle.

[0067] During the iterative optimization process, each particle records its own historical best position with the minimum fitness value, denoted as the individual extreme value. Simultaneously, the entire population records the globally optimal position with the minimum fitness value experienced by all particles, denoted as the global extreme value g. best Particles update their velocity and position based on individual and global extrema. The velocity update formula is:

[0068]

[0069] Where: v i (t+1) represents the velocity of the i-th particle in the (t+1)-th iteration; w represents the inertia weight, used to control the particle's ability to maintain its motion state from the previous moment. A larger w is beneficial for global exploration, while a smaller w is beneficial for local exploration; v i (t) represents the velocity of the i-th particle in the t-th iteration; c1 represents the individual learning factor, which adjusts the step size of the particle as it moves toward its historical best position. In this embodiment, it is preferably set to 2; r1 represents a random number distributed in the interval [0, 1]. x represents the optimal position found so far by the i-th particle, i.e., the individual extreme value; i(t) represents the current position of the i-th particle in the t-th iteration; c2 represents the social learning factor, which adjusts the step size of the particle as it moves toward the global optimal position of the group, and is preferably set to 2 in this embodiment; r2 represents another random number distributed in the interval [0, 1]; g best This represents the global optimal position found so far by the entire particle swarm, i.e., the global extreme value.

[0070] To further balance the algorithm's global search capability in the early stages of iteration with its local fine-tuning capability in the later stages, this embodiment preferably uses linearly decreasing weights.

[0071] The strategy is to dynamically adjust w. Specifically, the formula for how w changes with the number of iterations t is:

[0072]

[0073] Where: w max Set to 0.9; w min Set to 0.4; t is the number of iterations; t max This represents the maximum number of iterations. This dynamic adjustment mechanism ensures that the particle swarm can quickly cover the solution space in the early stages, and then stably converge to the vicinity of the optimal solution in the later stages.

[0074] Based on the updated velocity, the particle updates its current position coordinates by adding the current position to the updated velocity vector to obtain the position at the next moment.

[0075] By repeatedly executing the fitness calculation, extreme value update, and velocity and position update steps described above, the preset maximum number of iterations is reached or the global optimal fitness value satisfies the convergence condition. At this point, the final global optimal position g is output. best The 46 components are extracted and assigned to the BP neural network as optimal initial weights and biases. Then, based on these optimized initial parameters, the backpropagation training phase of the BP neural network is initiated, and the weights are further fine-tuned according to the gradient descent principle until the network converges.

[0076] See attached document Figure 5 After the Particle Swarm Optimization (PSO) algorithm outputs the globally optimal position parameters, this embodiment enters the second stage of joint training. This stage combines the global search capability of the PSO algorithm with the local optimization characteristics of the Backpropagation (BP) algorithm, using the error backpropagation algorithm to perform gradient descent optimization of the network parameters to construct the final prediction model for large deformation of soft rock tunnels.

[0077] First, perform parameter passing between the PSO and BP algorithms. The global extremum g output from the previous stage is then passed to the PSO algorithm. best(Containing data in 46 dimensions) is used as the initial weights and threshold of the BP neural network. Specifically, this vector is sequentially decoded and assigned to the connection weights w from the input layer to the hidden layer. ij The connection weights v from the hidden layer to the output layer jk Hidden layer bias b j and output layer bias b k At this point, the BP neural network no longer uses randomly initialized parameters, but instead uses the PSO-optimized solution as the starting point for training.

[0078] The iterative training of the BP neural network is initiated, a process that includes forward propagation of the signal and backward propagation of the error. After the data is input, the prediction error of the network is first calculated, which is the mean square error between the actual predicted output value of the neural network and the corresponding true expected value.

[0079] When the error does not meet the preset accuracy or the maximum number of training iterations is not reached, the correction amount for the weights of each layer is calculated according to the gradient descent principle. Specifically, the partial derivative of the error function with respect to the connection weights and biases of each layer is used to obtain the negative gradient direction, and the adjustment amount of the connection weights and biases is set to be proportional to this negative gradient. A learning rate is introduced into the calculation to control the adjustment step size.

[0080] Based on the calculated correction increment, update the connection weights from the input layer to the hidden layer, from the hidden layer to the output layer, and the bias values ​​of each layer to complete one iteration.

[0081] Repeat the above forward calculation, error assessment, and backward correction steps until the mean square error E of the network is reached. k Less than the preset convergence threshold (e.g., 10) -6 The training can continue until the preset number of iterations is reached. After training, the final weights and bias matrices are used to predict the validation set or new geological conditions. Since the network output is a normalized value, it needs to be normalized (Min-Max inverse transform) to restore it to the actual surrounding rock deformation value (unit: mm), thereby achieving quantitative prediction and early warning of large deformation in soft rock tunnels.

[0082] See attached document Figure 6 After using particle swarm optimization and backpropagation algorithms to jointly train the neural network, in order to verify the generalization ability and reliability of the generated large deformation prediction model for soft rock tunnels, it is necessary to introduce an independent test sample set for performance evaluation, and deploy the model on the actual engineering site for forecasting and early warning based on the evaluation results.

[0083] This embodiment first loads test sample data independent of the training set. This data includes seven-dimensional geological construction parameters (surrounding rock water content, construction method, support conditions, tunnel depth, surrounding rock dip angle, surrounding rock layer thickness, and lateral pressure coefficient) originating from the same source as the training set, along with the corresponding actual on-site monitored deformation. To eliminate differences between different dimensions of the input data and ensure the convergence of network training, this embodiment processes the input data using the Min-Max regularization method. For any input feature data x, its normalized value x... normalize .

[0084] The normalized test data is input into the trained PSO-BP neural network model to obtain the normalized prediction output value. In order to quantitatively evaluate the predictive performance of the model, this embodiment selects mean squared error (MSE), root mean square error (RMSE), and correlation coefficient (R^2) as core evaluation indicators according to the determined evaluation system.

[0085] Mean squared error (MSE) reflects the expected value of the squared difference between the predicted and actual values, and is used to measure the dispersion of model error. Its calculation formula is:

[0086] The root mean square error (RMSE) is the arithmetic square root of the mean square error. It is sensitive to outliers and can directly reflect the actual magnitude of the prediction error. Its calculation formula is:

[0087] The correlation coefficient measures the degree of linear correlation between model predictions and actual values. The closer the value is to 1, the better the model fits the data. Its calculation formula is:

[0088] Where: MSE represents the mean square error; RMSE represents the root mean square error; R 2 The coefficient represents the correlation coefficient; q represents the total number of samples in the test sample set. y represents the predicted output value of the neural network for the e-th sample; e This represents the actual value of the monitored deformation corresponding to the e-th sample; This represents the arithmetic mean of the actual monitored deformation of all test samples.

[0089] When the prediction accuracy of the PSO-BP model is confirmed to meet engineering requirements based on the above indicators (e.g., achieving R in this embodiment), 2 After achieving a goodness-of-fit of approximately 0.97, the PSO-BP model was applied to predict and warn of large deformations in actual engineering projects.

[0090] In the engineering application phase, seven-dimensional geological construction parameters of the section to be excavated ahead of the current tunnel face are obtained through on-site investigation. These parameters are then normalized using the Min-Max formula before being input into the model. After the normalized prediction results are output from the model, an inverse normalization operation must be performed to obtain the physically meaningful final deformation convergence value. The inverse normalization formula is:

[0091]

[0092] Where: Y predict This represents the final output of the predicted large deformation of the tunnel surrounding rock, i.e., the final deformation convergence value (unit: mm). Y represents the normalized predicted value of the PSO-BP neural network output; max Y represents the maximum deformation in the training sample set; min This represents the minimum deformation in the training sample set.

[0093] Obtain the predicted final deformation convergence value Y predict Then, it is compared with the reserved deformation amount or allowable deformation limit specified in the tunnel design code. If Y predict If the deformation exceeds the pre-set limit, it is determined that there is a risk of large deformation exceeding the limit. Simultaneously, based on real-time on-site monitoring data, the evolution curve formula is used... The trend of the monitored data is fitted, and the limit value obtained from the fitting is compared with the Y predicted by the neural network. predict A dual verification process is implemented. If both verifications indicate that the deformation will exceed the control standard, a large deformation warning is issued in a timely manner, guiding the construction team to control risks by increasing the initial support stiffness, adjusting construction methods, or implementing advanced support, thereby achieving data-driven safety management for soft rock tunnel construction.

Claims

1. A method for predicting large deformation of soft rock tunnels based on particle swarm optimization neural networks, characterized in that, Includes the following steps: S1. Determine the input factors that affect the large deformation of soft rock tunnels. The input factors specifically include geological construction characteristic parameters, and set the geological construction characteristic parameters as input layer variables of the neural network. S2. Obtain engineering sample data containing the input factors and the corresponding large deformation convergence values ​​of the surrounding rock, and normalize the engineering sample data using the minimum-maximum normalization algorithm to form a standardized neural network input matrix. S3. Construct an initial model of the backpropagation neural network for error, and use the particle swarm optimization algorithm to perform global iterative optimization of the connection weights and biases of the initial model. Set the network prediction error as the fitness value, search for the global optimal position vector and parse it into the optimal initial connection weights and optimal initial biases to complete the construction of the particle swarm optimization neural network model. S4. Input the normalized engineering sample data into the particle swarm optimization neural network model for error backpropagation training to generate a mature prediction model for large deformation of soft rock tunnels. Input the normalized geological construction data to be predicted into the mature prediction model for large deformation of soft rock tunnels, output the deformation prediction results and provide engineering early warning.

2. The method for predicting large deformation of soft rock tunnels based on particle swarm optimization neural networks according to claim 1, characterized in that, In step S1, the specific input factors affecting the large deformation of soft rock tunnels are determined as follows: The surrounding rock moisture content, tunnel construction method, tunnel support conditions, tunnel burial depth, surrounding rock dip angle, surrounding rock layer thickness, and lateral pressure coefficient are selected as the geological construction characteristic parameters. Furthermore, for the tunnel construction method and the tunnel support conditions, which are non-continuous qualitative variables, a mapping relationship between corresponding qualitative indicators and quantitative integer values ​​is established respectively.

3. The method for predicting large deformation of soft rock tunnels based on particle swarm optimization neural networks according to claim 1, characterized in that, In step S2, obtaining engineering sample data containing the input factors and corresponding large deformation convergence values ​​of the surrounding rock specifically involves: Based on the principle of orthogonal experimental design, typical level values ​​of various input factors are selected to construct orthogonal combined working conditions. Numerical simulation software is used to simulate and calculate each group of orthogonal combined working conditions, extract the maximum deformation convergence value under each working condition, construct a sample dataset containing the input factors and the large deformation convergence value of the surrounding rock, and use the sample dataset as the engineering sample data.

4. The method for predicting large deformation of soft rock tunnels based on particle swarm optimization neural networks according to claim 1, characterized in that, In step S2, the normalization process for the engineering sample data using the min-max normalization algorithm is specifically as follows: Calculate the maximum and minimum values ​​of each input factor in the engineering sample data across the entire dataset, calculate the difference between the value of the input factor in the current sample and the minimum value, calculate the difference between the maximum and the minimum value, and use the ratio of the two calculated differences as the normalized engineering sample data.

5. The method for predicting large deformation of soft rock tunnels based on particle swarm optimization neural networks according to claim 1, characterized in that, In step S3, the initial model of the error backpropagation neural network is constructed as follows: A three-layer neural network is constructed. The number of nodes in the input layer corresponds to the number of input factors, and the number of nodes in the output layer corresponds to the number of convergence values ​​of large deformation of the surrounding rock. The number of nodes in the hidden layer is determined by empirical formulas. The hidden layer adopts a logarithmic sigmoid transfer function, and the output layer adopts a linear transfer function, thereby completing the construction of the initial model of the error backpropagation neural network.

6. The method for predicting large deformation of soft rock tunnels based on particle swarm optimization neural networks according to claim 1, characterized in that, In step S3, during the global iterative optimization of the connection weights and biases of the initial model using the particle swarm optimization algorithm, the specific method for constructing the particle position vectors representing the connection weights and biases is as follows: The connection weight matrix from the input layer to the hidden layer, the bias vectors of each node in the hidden layer, the connection weight matrix from the hidden layer to the output layer, and the bias vectors of the nodes in the output layer are concatenated in sequence in the initial model of the backpropagation neural network to form the particle position vector in high-dimensional real vector form.

7. The method for predicting large deformation of soft rock tunnels based on particle swarm optimization neural networks according to claim 1, characterized in that, In step S3, the specific operation of using the particle swarm optimization algorithm to perform global iterative optimization of the connection weights and biases of the initial model is as follows: The position and velocity of each particle in the population are initialized, the fitness value of each particle is calculated, and the individual historical extreme value and the global extreme value of the population are updated. The velocity vector and position vector of the particles are dynamically updated according to the inertia weight, individual learning factor and social learning factor using a linear decreasing strategy, until the iteration termination condition is met, thereby completing the search for the global optimal position vector.

8. The method for predicting large deformation of soft rock tunnels based on particle swarm optimization neural networks according to claim 1, characterized in that, Step S4, which involves backpropagation training, specifically involves: Based on the optimal initial connection weights and the optimal initial bias to start the network, the prediction error of the forward propagation of the particle swarm optimization neural network model is calculated. The correction increment of the connection weights and biases of each layer is calculated according to the gradient descent principle. The network parameters are updated using the correction increments. The process is repeated until the mean square error is less than a preset threshold, thereby generating the mature large deformation prediction model for soft rock tunnels.

9. The method for predicting large deformation of soft rock tunnels based on particle swarm optimization neural networks according to claim 1, characterized in that, In step S4, the specific output deformation prediction result is as follows: The inverse normalization process is performed by multiplying the normalized predicted value output by the mature soft rock tunnel large deformation prediction model by the difference between the maximum and minimum values ​​of the large deformation convergence value of the surrounding rock in the engineering sample data, and then adding the minimum value to the value obtained by multiplication to restore the final deformation prediction value with physical length units.

10. A method for predicting large deformation of soft rock tunnels based on particle swarm optimization neural networks according to claim 9, characterized in that, In step S4, the specific steps for issuing an engineering early warning are as follows: A dual verification mechanism is adopted to compare the final deformation prediction value with the tunnel design allowance deformation amount, and to compare it with the evolution curve limit value fitted by the on-site monitoring data. When both show that the deformation amount will exceed the safety allowable standard, a large deformation graded early warning signal is issued, thereby completing the engineering early warning.

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