A large-diameter full-precast assembled shield tunneling posture intelligent prediction method

By using the improved ADWPSO algorithm and GRU neural network, an intelligent prediction model for shield tunnel excavation posture was constructed, which solved the uncertainty problem of parameter prediction in large-diameter shield tunnel excavation and achieved efficient and accurate construction control.

CN118690645BActive Publication Date: 2025-11-21CCCC TUNNEL ENG CO LTD +1
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Patent Information

Application Number
CN202410789907.4
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-06-18
Publication Date
2025-11-21
Estimated Expiration
2044-06-18

AI Technical Summary

Technical Problem

Existing technologies lack scientific and reasonable prediction models for tunneling parameters in large-diameter shield tunneling, leading to uncertainties in construction progress and safety quality. In particular, when considering special construction techniques such as curved components and central partition walls, the complexity of the models and the low computational efficiency affect the construction control effect.

Method used

An improved ADWPSO algorithm combined with a gated recurrent unit (GRU) neural network is used to construct an intelligent prediction model. Through feature vector selection and data preprocessing, the nonlinear relationship of shield attitude parameters is identified, thereby improving computational efficiency and accuracy.

Benefits of technology

It enables accurate prediction of the tunneling posture of large-diameter shield tunnels, reduces the impact of human factors, improves construction efficiency and quality, and allows for timely adjustment of construction parameters to avoid abnormal risks.

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Abstract

The present application relates to the technical field of shield construction, in particular to a large-diameter shield full-precast assembly tunneling posture intelligent prediction method. The steps are as follows: (1) constructing a gated recurrent unit neural network and selecting a feature vector; (2) preprocessing the original data set, first performing data noise reduction, and then uniformly performing normalization processing; (3) dividing the training set, the validation set and the test set according to a certain proportion; (4) constructing an inertia weight dynamic updating formula based on the perturbation state theory, and proposing an adaptive perturbation weight particle swarm optimization algorithm for determining the optimal hyperparameter combination of the gated recurrent unit network; and the like. The present application can reveal the complex nonlinear mapping relationship between the tunneling parameters and the posture parameters under the large-diameter full-precast assembly process; at the same time, the improved ADWPSO algorithm improves the calculation efficiency and accuracy of the prediction model.
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Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of shield construction, in particular to a large-diameter shield full-precast assembly tunneling posture intelligent prediction method. BACKGROUND

[0002] As an efficient, environmentally friendly and safe engineering construction method, the shield method has been widely used in urban rail transit construction. The precast assembly technology of the outer segment of the shield tunnel is quite mature, and gradually develops towards large diameter, high burial depth and long distance. With the development of concrete precast components and shield equipment construction technology in China, the precast assembly of the internal structure of large-diameter shield tunnels has attracted more and more attention. In the process of shield tunneling, the setting of tunneling parameters is mainly based on the subjective experience of the shield driver, and there is a lack of reasonable prediction of tunneling parameters, which has a great uncertainty and affects the progress and safety quality of construction. The shield posture is a construction parameter that needs to be strictly controlled in the process of tunneling, and if it is not properly controlled, it will lead to excessive settlement of the ground surface, difficulty in tunneling, cracking of the segment and other engineering problems. In order to realize the fine operation in the process of shield tunneling and reduce the influence of human subjective factors, it is urgent to establish a scientific and reasonable intelligent prediction model of shield tunneling posture.

[0003] Based on machine learning algorithm, the establishment of shield tunneling posture prediction model has become a hot issue in recent years. The existing research mainly considers the influence of construction parameters, stratum parameters and tunnel structure parameters on the prediction of shield posture by using methods such as support vector machine (SVM), long short-term memory network (LSTM) and convolutional neural network (CNN) to guide the construction. However, the above methods cannot consider the high nonlinearity and complexity between parameters caused by special construction processes such as arc-shaped parts and middle partitions in large-diameter full-precast assembly shield tunnels, which are prone to feature redundancy and other problems, and with the increase of data volume, the model structure is complex and the parameters are increased, which affects the calculation efficiency and accuracy, and poses a greater challenge to the control of shield tunneling posture. SUMMARY

[0004] The present application comprehensively considers the influence of shield tunneling, stratum and tunnel parameters, and designs a large-diameter full-precast assembly shield tunneling posture intelligent prediction method, which can identify the related variables having a high nonlinearity with the shield posture parameters under the influence of special construction processes such as arc-shaped parts and middle partitions, and improve the calculation efficiency and accuracy of the prediction model through the improved ADWPSO algorithm, so that the field operators can adjust the operation in time according to the real-time prediction data of the shield posture to avoid the risk of abnormal posture.

[0005] It is of great significance to ensure the engineering quality and construction efficiency.

[0006] The present application adopts the following technical scheme:

[0007] A large-diameter full-precast assembled shield tunneling posture intelligent prediction method is characterized by the following steps:

[0008] (1) A gated recurrent unit (GRU) neural network is constructed and a feature vector is selected; specifically, sample original data is collected, a gated recurrent unit (GRU) is selected to construct a prediction model based on the time series characteristics of the shield posture data;

[0009] (2) The original data set is preprocessed, first data denoising is performed, and then normalization processing is uniformly performed;

[0010] (3) The training set, the validation set and the test set are divided according to a certain proportion;

[0011] (4) Based on the disturbance state theory, an inertia weight dynamic updating formula is constructed, and an adaptive disturbance weight particle swarm optimization (ADWPSO) algorithm is proposed to determine the optimal hyperparameter combination of the gated recurrent unit (GRU) network;

[0012] (5) Based on the prediction model constructed in step (1) and the optimal hyperparameter combination established by the adaptive disturbance weight particle swarm optimization (ADWPSO) algorithm designed in step (4), an ADWPSO-GRU prediction model is established, which can dynamically output the shield posture prediction value according to the continuously updated sample data set.

[0013] The present application can comprehensively consider the influence of stratum conditions-tunnel structure-tunneling parameters, identify parameter variables with high non-linear relationship with shield posture parameters under the influence of special assembly processes such as arc-shaped parts and partition walls, i.e. it can reveal the complex non-linear mapping relationship between tunneling parameters and posture parameters under the large-diameter full-precast assembly process. At the same time, the improved ADWPSO algorithm improves the calculation efficiency and accuracy of the prediction model. Therefore, the present application has great application value. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 Flowchart of the large-diameter shield full-precast assembled tunneling posture intelligent prediction method of the present application

[0015] Figure 2 GRU unit internal structure and prediction model architecture diagram of the present application: (a) GRU unit internal structure; (b) GRU neural network prediction model architecture

[0016] Figure 3 ADWPSO algorithm used in the present application and standard PSO algorithm optimization effect comparison

[0017] Figure 4 Shield tunneling posture prediction results in the example (taking the cutter head vertical deviation as an example) DETAILED DESCRIPTION

[0018] The implementation process of the present application is described in detail below, referring to Figure 1 , and the specific implementation steps are as follows:

[0019] (1) Construct a gated recurrent unit (GRU) neural network and select a feature vector; specifically, collect sample original data, select a gated recurrent unit (GRU) to construct a prediction model based on the time series characteristics of the shield posture data;

[0020] The gated recurrent unit (GRU) is selected to construct a prediction model, referring to Figure 2 Specifically:

[0021] It includes an input layer, a gated recurrent unit (GRU) layer, and a fully connected layer.

[0022] First, input the time series characteristic data x t through the input layer into the gated recurrent unit (GRU) layer.

[0023] Each GRU in the gated recurrent unit (GRU) layer mainly includes two gating structures, a reset gate and an update gate.

[0024] The reset gate r t is the concatenation of the hidden state h t-1 of the previous time step and the input data x t of the current time step, and is expressed by a Sigmoid function h t-1 The saved proportion is expressed by the following formula:

[0025] r t =σ(W r ·[h t-1 ,x t ]+b r )

[0026] In the formula, [] represents the concatenation of the matrix; W and b represent the weight matrix and the bias term, respectively; and σ is the Sigmoid activation function.

[0027] After the reset gate calculation, the hidden layer candidate state u t of the current time step can be obtained, and the calculation formula is as follows:

[0028] u t =tanh(W h ·[r t ×h t-1 ,x t ]+b h )

[0029] Similar to the reset gate, the update gate z t is also the concatenation of ht-1 and x t is expressed by the following formula:

[0030] z t = σ(W z · [h t-1 , x t ] + b z )

[0031] The hidden state h t at the current time step is determined by z t , h t-1 and u t , and is expressed by the following formula:

[0032] h t = (1-z t ) x h t-1 + z t x u t

[0033] Finally, the shield attitude prediction value y is output by transforming through the fully connected layer, including four attitude parameters of cutter head horizontal deviation y1, cutter head vertical deviation y2, shield tail horizontal deviation y3 and shield tail vertical deviation y4.

[0034] Among them, the network input parameters include stratum parameters, tunnel geometric parameters and tunneling parameters. The stratum parameters are specific gravity γ, compression modulus E s , cohesion C, friction angle and static earth pressure coefficient K; the tunnel geometric parameter selects the ratio H / D of tunnel buried depth H and tunnel diameter D; considering the influence of special construction technology such as partition wall and arc-shaped part in large-diameter full-precast assembled shield tunnel, the first five tunneling parameters (j1, j2, j3, j4, j5) having strong nonlinear relationship with the shield attitude target value are selected by mutual information feature selection algorithm, and are combined with the stratum parameters tunnel geometric parameter (H / D) to form the input data set x. The network output parameter is the shield attitude parameter, including four attitude parameters of cutter head horizontal deviation y1, cutter head vertical deviation y2, shield tail horizontal deviation y3 and shield tail vertical deviation y4;

[0035] Among them, the mutual information feature value can be calculated according to the following formula:

[0036]

[0037] In the formula, P(X, Y) represents the joint probability distribution of random variables X and Y; P(X) and P(Y) represent the marginal probability distribution of random variables X and Y, respectively;

[0038] (2) The original data set is preprocessed, first data denoising, and then unified normalization processing;

[0039] wherein the data denoising adopts the Laplace (3σ) criterion to perform outlier screening on the original data, and eliminates the historical data corresponding to the shield machine stopping motion; then normalization processing is performed;

[0040] wherein the normalization processing can be calculated according to the following formula:

[0041]

[0042] wherein X norm is the normalized parameter value; X max is the maximum value in the parameter; X min is the minimum value in the parameter;

[0043] (3) The training set, the validation set and the test set are divided according to the principle of 6:2:2;

[0044] wherein the training set and the validation set are mainly used to update the network parameters and debug the hyperparameters, and the test set is used to evaluate the model performance;

[0045] wherein the performance evaluation of the prediction model respectively adopts the accuracy and the goodness of fit R 2 two indexes.

[0046] wherein the accuracy selects three error tolerance levels: ε = 10%, ε = 15%, ε = 25%, that is, the measured value v and the predicted value v p in the test set can satisfy the following formula, then it is considered that the result of the prediction model on the sample is accurate:

[0047] v(1-ε)≤v p ≤v(1-ε)

[0048]

[0049] wherein m p is the number of samples in the model prediction value that meet the error tolerance level; m is the total number of samples in the test set.

[0050] The goodness of fit R 2 can be calculated according to the following formula:

[0051]

[0052] wherein y is the calculation value of the prediction model for the lth sample in the test set; y l is the actual value of the lth sample in the test set; is the average value of all samples in the test set;

[0053] (4) Based on the disturbance state theory, an inertia weight dynamic updating formula is constructed, and an adaptive disturbance weight particle swarm optimization (ADWPSO) algorithm is proposed to determine the optimal hyperparameter combination of the gated recurrent unit (GRU) network;

[0054] wherein the adaptive disturbance weight particle swarm optimization (ADWPSO) algorithm determines the optimal hyperparameter combination of the gated recurrent unit (GRU) network;

[0055] wherein the optimal hyperparameter combination of the GRU network model mainly includes a data window size, a number of hidden layer neurons, a learning rate, and a regularization parameter, i.e., a hyperparameter dimension D = 4;

[0056] Based on the disturbance state theory, an adaptive inertia weight dynamic updating formula is constructed to adjust the particle velocity and position;

[0057] wherein the velocity and position updating formula of the dth dimension optimization subspace of the particle i in the population when updated to the kth generation is as follows:

[0058]

[0059] In the formula, w is an inertia weight, which determines the degree of change of the current particle velocity; c1 and c2 are respectively an individual and a social learning factor, which can balance the influence effect of the particle and the global optimal position; r1 and r2 are random numbers between 0 and 1; is the individual optimal position searched by the dth dimension of the ith particle at the end of the kth iteration; is the global optimal position of the dth dimension of the entire particle swarm at the end of the kth iteration, and the optimal solution of the hyperparameters (data window size, number of hidden layer neurons, learning rate, and regularization parameter) can be output when the iteration termination condition is reached;

[0060] wherein the change of the inertia factor w determines the search ability of the particle, and the adaptive weight dynamic updating formula is established by introducing the disturbance state theory to balance the global and local search abilities:

[0061]

[0062] In the formula, is a disturbance factor; w max and w min are the maximum and minimum inertia factors, respectively taking 0.9 and 0.4;

[0063] wherein the disturbance factor can be expressed by the following formula:

[0064]

[0065] In the formula, A parameter for representing a relative change rate of the fitness value of the particle;

[0066] Parameter The parameter can be determined by the following formula:

[0067]

[0068] In the formula, is the fitness value of the particle i at the kth iteration.

[0069] (5) An ADWPSO-GRU prediction model is established, and the shield posture prediction value can be dynamically output according to the continuously updated sample data set.

[0070] The application will be further described below by examples.

[0071] Please refer to Figure 1 The embodiment provides a large-diameter full-precast assembled shield tunneling posture intelligent prediction method, and the large-diameter full-precast assembled shield tunneling posture prediction in Shanghai is taken as an example for illustration.

[0072] Firstly, based on the time sequence characteristics of the shield posture data, a gated recurrent unit (GRU) is selected to construct a prediction model, and sample data are collected, wherein input parameters include stratum parameters, tunnel geometric parameters and tunneling parameters. The stratum parameters are specific gravity γ, compression modulus E s , cohesion C, friction angle and static earth pressure coefficient K; the tunnel geometric parameter is the ratio H / D of the tunnel buried depth H to the tunnel diameter D; considering the influence of the special construction process such as the partition wall and the arc-shaped part in the large-diameter full-precast assembled shield tunnel, the first five tunneling parameters (j1, j2, j3, j4 and j5) having a strong nonlinear relationship with the shield posture target value are selected through a mutual information feature selection algorithm, and are combined with the stratum parameters and the tunnel geometric parameter (H / D) to form an input data set x. The output parameter is a shield posture parameter, including a cutter head horizontal deviation y1, a cutter head vertical deviation y2, a shield tail horizontal deviation y3 and a shield tail vertical deviation y4.

[0073] Secondly, the original data set is preprocessed, that is, data noise reduction is performed, and then normalization processing is uniformly performed.

[0074] According to the principle of 6:2:2, a training set, a validation set and a test set are divided. The training set and the validation set are mainly used to update network parameters and debug hyperparameters, and the test set is used to evaluate the performance of the model. The performance evaluation of the prediction model adopts accuracy and goodness of fit R 2 two indexes.

[0075] The optimal hyperparameter combination for a gated recurrent unit (GRU) network is determined based on the Adaptive Perturbation Weighted Particle Swarm Optimization (ADWPSO) algorithm. Specifically, the search dimension D of the ADWPSO algorithm is set to 4, and the maximum inertia weight is set to w. max =0.9, minimum inertia weight is w min =0.4, the individual learning factor is set to c1=2, and the social learning factor is set to c2=2. Meanwhile, to ensure high accuracy and stability of the model, the number of particles was determined to be 10 and the number of iterations to be 50 through multiple experiments.

[0076] Taking the sample dataset corresponding to the vertical deviation of the cutterhead y2 as an example, the ADWPSO algorithm is used to determine the optimal hyperparameters of the GRU network model in the current case, namely the data window size, the number of hidden layer neurons, the learning rate, and the dropout ratio. The final values ​​are 2, 35, 0.002, and 0.08, respectively. (The steps for establishing the prediction models for the other cutterhead horizontal deviation y1, shield tail horizontal deviation y3, and shield tail vertical deviation y4 are the same. Only the corresponding sample dataset needs to be changed, which will not be repeated here.)

[0077] The ADWPSO algorithm and the traditional PSO algorithm are used to compare the hyperparameter optimization process. Figure 3 As shown, the fitness of the ADWPSO algorithm converges at approximately 14 generations and its value becomes smaller, while the fitness of the traditional PSO algorithm converges around 25 generations. These results indicate that the ADWPSO algorithm can dynamically adjust the weights by considering the algorithm's performance feedback parameters, effectively balancing the global and local search capabilities at different stages of the algorithm.

[0078] Finally, the optimal hyperparameter combination determined by the ADWPSO algorithm is used to construct a GRU prediction model, which can output shield attitude prediction data based on continuously updated sample data. Figure 4 It can be seen that the predicted shield attitude based on ADWPSO-GRU can fit the measured value curve well. The prediction accuracy reaches 0.823, 0.924 and 0.961 under the allowable error of 10%, 15% and 25% respectively, and the goodness of fit R is 0.823, 0.924 and 0.961 respectively. 2 The accuracy reached 0.912. The results show that the shield attitude prediction model proposed in this paper can effectively take into account the characteristics of large-diameter fully prefabricated assembly construction technology, improve the prediction accuracy and efficiency of the model, provide a reliable reference for shield tunneling construction, and assist on-site operators in timely correcting construction parameters to avoid risks such as abnormal attitude.

Claims

1. A method for intelligent prediction of the excavation posture of a large-diameter, fully prefabricated shield tunnel, characterized in that, Implement the following steps: (1) Constructing a gated recurrent unit (GRU) neural network and selecting feature vectors; Specifically, collecting raw sample data, and selecting gated recurrent units (GRU) to construct a prediction model based on the time series features of shield attitude data; (2) Preprocess the original dataset by first reducing noise and then normalizing it. (3) Divide the training set, validation set, and test set according to a certain ratio; (4) Based on the perturbation state theory, an inertial weight dynamic update formula is constructed, and an adaptive perturbation weight particle swarm optimization (ADWPSO) algorithm is proposed to determine the optimal hyperparameter combination of the gated recurrent unit (GRU) network. (5) Based on the prediction model designed in step (1) and the optimal hyperparameter combination established by the adaptive perturbation weighted particle swarm optimization (ADWPSO) algorithm designed in step (4), the ADWPSO-GRU prediction model was established, which can dynamically output the shield attitude prediction value according to the continuously updated sample dataset. In step (1), the influence of special construction techniques such as partition walls and curved components in large-diameter fully prefabricated shield tunnels is considered. The top five tunneling parameters with strong nonlinear relationships to the shield attitude target value are selected by mutual information feature selection algorithm. j 1. j 2. j 3. j 4. j 5), and with formation parameters ( , E s , C , , K ), tunnel geometric parameters ( H / D ), participate in forming the input dataset x ; The mutual information feature value can be calculated according to the following formula: In the formula, P ( X , Y ) represents a random variable X and Y The joint probability distribution of ; P ( X )and P ( Y ) represent random variables respectively X and Y The marginal probability distribution; The Adaptive Perturbation Weighted Particle Swarm Optimization (ADWPSO) algorithm established in step (4) is used to determine the optimal hyperparameter combination of the gated recurrent unit (GRU) network. The optimal combination of hyperparameters for the GRU network model mainly includes the data window size, the number of hidden layer neurons, the learning rate, and the regularization parameter, i.e., the hyperparameter dimensions. D =4; Specifically, The Adaptive Perturbation Weighted Particle Swarm Optimization (ADWPSO) algorithm: An adaptive inertial weight dynamic update formula is established based on the perturbation state theory to adjust particle velocity and position; Among them, particles in the population i Updated to the k In the era, the first d The velocity and position update formulas for the optimal subspace are as follows: In the formula, w The inertial weight determines the degree of change in the current particle velocity; c 1 and c 2 represents individual and social learning factors, which can balance the effects of the optimal position of particles and groups; r 1 and r 2 is a random number between (0, 1); For the first d Vi in the i The particle to the first k The optimal position of the individual found at the end of the next iteration; For the entire particle swarm in the th k At the end of the iteration, the... d The global optimal position of the dimension can be found, and the optimal solution of hyperparameters (data window size, number of hidden layer neurons, learning rate and regularization parameter) can be output when the iteration termination condition is met; w The change in inertia factor determines the particle's search capability. To balance global and local search capabilities, perturbation state theory is introduced to establish an adaptive weight dynamic update formula: In the formula, For disturbance factors; w max and w min The maximum and minimum inertia factors are set to 0.9 and 0.4, respectively. Among them, the disturbance factor It can be expressed by the following formula: In the formula, A parameter characterizing the relative rate of change of particle fitness; parameter Determined by the following formula: In the formula, For particles i exist k The fitness value at the next iteration.

2. The intelligent prediction method for the excavation attitude of a large-diameter fully prefabricated shield tunnel as described in claim 1, characterized in that, In step (1), the feature vector is selected and designed as follows: The network input parameters include geological parameters, tunnel geometry parameters, and tunneling parameters; The specific formation parameters are: unit weight Compression modulus E s Cohesion C Friction angle and coefficient of earth pressure at rest K ; Tunnel geometric parameters selection and tunnel burial depth H With tunnel diameter D ratio H / D ; The tunneling parameters are selected using a mutual information feature selection algorithm to identify variables that are strongly correlated with the network output parameters; the network output parameters are the shield attitude parameters, including the cutterhead horizontal deviation. y 1. Vertical deviation of the cutter head y 2. Horizontal deviation of the shield tail y 3 and vertical deviation of the shield tail y 4. Four attitude parameters; The above parameters are selected from the collected raw sample data to form the input dataset. x, By data window size T To form a time series feature based on the shield tunneling attitude data, this time series feature data serves as the input data. x t .

3. The intelligent prediction method for the excavation posture of a large-diameter fully prefabricated shield tunnel as described in claim 1, characterized in that, In step (1), The selection of gated recurrent units (GRUs) to construct the prediction model specifically involves: It includes an input layer, a gated recurrent unit (GRU) layer, and a fully connected layer; First, input data with time series characteristics. x t The data is sent to the Gate Controlled Recurrent Unit (GRU) layer via the input layer; Each GRU in the Gated Cyclic Unit (GRU) layer mainly includes two gating structures: a reset gate and an update gate. Among them, the reset door r t It is to hide the state of the previous time step. h t-1 Input data at the current time step x t Concatenate them together and represent them using the Sigmoid function. h t-1 The proportion that is preserved is expressed by the following formula: In the formula, [] denotes the concatenation of matrices; W and b These represent the weight matrix and the bias term, respectively. Use the Sigmoid activation function; After resetting the gate calculation, the candidate hidden layer state at the current time step can be obtained. u t The calculation formula is as follows: Similar to resetting a door, updating a door z t It is also to h t-1 and x t When spliced ​​together, it can be represented by the following formula: The hidden state at the current time step h t Depend on z t , h t-1 and u t A joint decision, expressed by the following formula: Finally, the shield attitude prediction value is transformed through a fully connected layer. y Including cutter head horizontal deviation y 1. Vertical deviation of the cutter head y 2. Horizontal deviation of the shield tail y 3 and vertical deviation of the shield tail y 4. Four attitude parameters.

4. The intelligent prediction method for the excavation posture of a large-diameter fully prefabricated shield tunnel as described in claim 1, characterized in that, In step (2) of preprocessing, data denoising is performed using Laida (3 σ The criteria are used to filter out outliers from the raw data and remove historical data corresponding to when the tunnel boring machine stopped moving; then normalization is performed. The normalization process can be calculated using the following formula: In the formula, X norm These are the normalized parameter values; X max The maximum value among the parameters; X min It is the minimum value among the parameters.

5. The intelligent prediction method for the excavation posture of a large-diameter fully prefabricated shield tunnel as described in claim 1, characterized in that, In step (3), the training set, validation set, and test set are divided; The training and validation sets are mainly used to update network parameters and debug hyperparameters, while the test set is used to evaluate model performance. The performance evaluation of the prediction model uses accuracy and goodness of fit, respectively. R 2 Evaluation based on two indicators; The accuracy rate is selected based on three error tolerance levels: ε =10% ε =15% ε =25%, which is the measured value in the test set. v and predicted value v p If the following equation is satisfied, the prediction model is considered accurate on that sample: In the formula, m p This represents the number of samples in the model's predicted values ​​that meet the error tolerance level. m The total number of samples in the test set; Goodness of fit R 2 It can be calculated using the following formula: In the formula, For the prediction model on the test set l Calculated values ​​for each sample; For the first test set l The actual value of each sample; This is the average value of all samples in the test set.

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