A method for constructing a coefficient prediction model, a coefficient prediction method, and a storage medium

Abstract

The present disclosure relates to a method for constructing a coefficient prediction model, a coefficient prediction method and a storage medium. The method comprises the following steps: modeling a bridge prestressed beam and simulating a tensioning process by using finite element numerical software, constructing a bridge parameter coefficient array, dividing the array into a training data set and a validation data set, performing data standardization and tensor data conversion, and constructing a data loader; constructing a full connection multilayer multitask neural network based on TensorFlow, which is provided with a standardizer, a forward propagation function, a loss function, a learning rate scheduler, and an optimizer; performing model training, packaging a prediction function, integrating the standardizer and the trained prediction model. The prediction method comprises predicting the friction loss coefficient and the pipe deviation coefficient according to the prediction model. The present disclosure can quickly and efficiently and accurately realize coefficient prediction by using only a few easily measured parameters.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of machine learning of concrete engineering, and in particular to a construction method of a coefficient prediction model, a coefficient prediction method and a storage medium. BACKGROUND

[0002] In today's concrete engineering, prestressed concrete structures are widely used in various fields due to their excellent crack resistance, high bearing capacity and durability. In the prestressed construction process, there are various prestress losses, among which the duct friction loss is one of the main prestress loss items, usually accounting for about 30% to 50% of the total loss (according to the “Highway Reinforced Concrete and Prestressed Concrete Bridge and Culvert Design Specification” JTG 3362-2018 compiled by the China Communications Planning and Design Institute Co., Ltd. and published by the People's Communications Press in 2018), which directly affects the post-tensioning prestressed beam body camber, pre-compression stress and steel beam effective prestress, and further affects the final effective stress distribution of the beam body, the bearing capacity of the structure itself and the long-term performance. For this, there are currently five types of methods: theoretical formula method, specification simplification method, numerical iteration simulation method, field calibration method and empirical coefficient method. For the field calibration method and the empirical coefficient method, one is to directly measure in the field or laboratory with sensors, and the other is to estimate the initial tension control stress by percentage according to previous engineering experience. The former is tedious to operate, reduces construction efficiency and increases calculation cost, and the latter has low precision and is mainly used in preliminary design, which is not suitable for complex conditions or different sites.

[0003] The theoretical formula method is to calculate the friction loss value based on the formula recommended by the specification. For example, the relevant provisions of the prestressed friction loss in the “Concrete Structure Design Specification” (GB50010-2010) compiled by the China Academy of Building Science, jointly published by the Ministry of Housing and Urban-Rural Development of the People's Republic of China and the General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China. For example, the relevant provisions of the prestressed friction loss in the “Highway Reinforced Concrete and Prestressed Concrete Bridge and Culvert Design Specification” (JTG 3362-2018) compiled by the China Communications Planning and Design Institute Co., Ltd. and published by the People's Communications Press. For example, the relevant provisions of the prestressed friction loss in the “Prestressed Concrete Structure Design Specification” (JGJ 369-2016) published by the Standard Quota Research Institute and the China Construction Industry Press. The theoretical formula method itself is based on Coulomb's friction law, has clear physical meaning and comprehensive value, and is suitable for the design and calculation of most straight and curved prestressed reinforcement today. However, although the theoretical formula is simple and fast to calculate, it gives the friction loss coefficient and the pipe deviation coefficient as constants, to some extent, ignoring the construction errors and duct deformation factors in the engineering, sometimes it is difficult to reflect the true friction characteristics under complex conditions.

[0004] The code-simplified method is based on the above theoretical formula for simplified calculation, or directly determine the value of the friction loss of prestress by looking up table. Based on the theoretical formula method, it is simplified, and it also inherits the advantages of the theoretical formula method, while greatly reducing the cost of calculation, widely used in hand calculation or preliminary stage of design. But its qualitative model can not adapt to new materials, special process or extreme conditions, and the constant coefficient used in the theoretical formula method can not reflect the construction differences in specific engineering.

[0005] The numerical iterative simulation method is to establish the nonlinear finite element data model of prestressed tendon-pore contact by finite element software, and sometimes to use equivalent temperature method and other equivalent tension methods to simulate different linear segments.

[0006] The paper "Research on the friction loss of prestressed concrete beam bridge bending duct" published in the journal of Wuhan University (Engineering Edition) uses finite element analysis software to simulate the actual contact behavior of steel tendon and concrete, and finds that the prestressed friction loss changes with the bending angle, tension stress and friction loss coefficient, and the maximum contact pressure of the bending duct changes with the bending angle and tension force, which shows that there is a mutual coupling phenomenon among tension force, friction force and contact pressure, and reveals a new law of concrete contact pressure distribution that is more consistent with the actual working condition than the code.

[0007] The paper "Friction loss of pure bending duct under non-uniform pressure" published in the journal of Science, Technology and Engineering proposes a method to calculate the influence of tension control stress, prestressed tendon bending angle and duct friction loss coefficient on friction loss value in finite element software , and gives a more accurate derivation formula based on the simulation results.

[0008] However, the numerical iterative simulation method has high calculation precision and can simulate different nonlinear behaviors and output intuitive and visual results of prestressed tendon stress distribution or deformation, but the relative technical requirements are high, the calculation amount and cost increase sharply, and the simulation difficulty and time of large and complex structures increase dramatically, which requires high-performance computers. Sometimes it is difficult to balance the project period and construction efficiency, time benefit, calculation precision and cost.

[0009] Based on the advantages and disadvantages of numerical iterative simulation method, machine learning and numerical iterative simulation are combined to establish MLP neural network architecture and combine BP algorithm (back propagation algorithm), etc. Based on numerical simulation data, relevant prediction is carried out. In the field of engineering data prediction, machine learning can automatically capture complex nonlinear patterns and interactions in data without manually constructing mathematical models; can process multi-source multi-dimensional data and update the model adaptively to continuously optimize, which is more suitable for changing working conditions than static empirical formula; while balancing multiple tasks, it reduces the deviation of artificial modeling and speeds up the decision-making cycle.

[0010] In the prediction of the friction loss coefficient and the pipe deviation coefficient in the bridge prestress friction loss, the construction of the prediction model is based on parameter information that is difficult to obtain in actual engineering application, thereby making it difficult to realize prediction when the model is applied, affecting the application range and promotion of the model.

[0011] Therefore, the prior art has not provided a method for constructing a prediction model of the friction loss coefficient and the pipe deviation coefficient in the bridge prestress friction loss and a method for predicting the friction loss coefficient and the pipe deviation coefficient in the bridge prestress friction loss under the premise that the model parameters are easy to obtain. How to establish a training model combined with the indicators that are easy to obtain in actual engineering application and use it to predict different working conditions has become a problem to be solved. SUMMARY

[0012] Based on this, it is necessary to provide a method for constructing a coefficient prediction model and a coefficient prediction method and a storage medium in view of how to construct a coefficient prediction model in the bridge prestress friction loss in combination with the indicators that are easy to obtain in actual engineering application.

[0013] To solve the above problems, the present disclosure adopts the following technical solutions:

[0014] In a first aspect, the present disclosure provides a method for constructing a coefficient prediction model, comprising the following steps:

[0015] Step 1: using finite element numerical software to model the bridge prestressed beam and simulate the tensioning process, extracting the parameters of the bridge prestressed beam, the friction loss coefficient Information and pipe deviation coefficient Information, constructing a bridge parameter coefficient array; the parameters of the bridge prestressed beam include bridge span L, bridge height H, height distribution of prestressed tendon at fulcrum section position positioning point on beam height , including deflection of beam span under different prestress loss conditions , cross-section area of span and centroid of span cross-section ;

[0016] Step 2: Divide the bridge parameter coefficient array into a training dataset and a validation dataset. Perform data standardization and tensor data transformation on both the training dataset and the validation dataset in sequence, and build a data loader.

[0017] Step 3, build based on and A fully connected multilayer multitasking neural network with activation function is used to predict friction loss coefficients. and pipeline deviation coefficient The prediction model, wherein the fully connected multilayer multitasking neural network includes a normalizer, a forward propagation function, and loss function Learning rate scheduler Optimizer;

[0018] Step 4: Define the training function, validation function, and training process monitoring function. Based on the fully connected multi-layer multi-task neural network and the data loader, train the prediction model to obtain the trained prediction model. Encapsulate the prediction function, integrate the normalizer and the trained prediction model, provide an interactive input interface, and form a prediction system.

[0019] In a preferred embodiment, step 1 includes analyzing the effect of each parameter in the bridge parameter coefficient array on the MLP regression model's prediction of the friction loss coefficient. Importance and Predictive Pipe Deviation Coefficient The importance of.

[0020] In a preferred embodiment, the step of constructing the bridge parameter coefficient array includes: creating a regular expression in file format for the extracted parameters, and constructing the bridge parameter coefficient array based on the regular expression.

[0021] In a preferred embodiment, the bridge parameter coefficient array is: Array, the data is standardized as Standardization, the tensor data is transformed into a standardized form. Array to Tensor.

[0022] In a preferred embodiment, the The loss function is:

[0023] ;

[0024] in: Indicates the training sample number, indicating the first training sample. One training sample; This represents the total number of training samples. For the model to the first Predicted values ​​for each training sample. For the first The true value of each training sample. for The numerical value of the loss function;

[0025] The model's total loss function is:

[0026] ;

[0027] in, This represents the hyperparameter balancing the relative importance of the loss terms. This represents the loss function with weighted penalty terms. Represents the total loss function;

[0028] The The optimizer satisfies:

[0029] ;

[0030] in, This represents the updated model parameters; Indicates the model parameters that need to be optimized; The learning rate; Represents the numerically stable term; This represents the first-order moment estimate of the gradient after bias correction; This is the second-order moment estimate of the gradient after bias correction; This is the weight decay coefficient;

[0031] The learning rate scheduler is as follows:

[0032] ;

[0033] in: This represents the learning rate adjusted by the learning rate scheduler. Indicates the current learning rate; For attenuation parameters; This is the lower limit of the learning rate; the scheduling strategy is triggered when the verification loss does not decrease within the patience value rounds.

[0034] In a preferred embodiment, step 4 further includes: making predictions using the trained prediction model, restoring the data dimensions through inverse standardization, and calculating evaluation indicators to evaluate the prediction model.

[0035] In a preferred embodiment, the fully connected multi-layer multi-task neural network comprises a shared feature extraction layer, a first independent task-specific layer and a second independent task-specific layer, each of which is provided with a normalizer, the input of the shared feature extraction layer is the parameter, and the output is the extracted shared feature, the input of the first independent task-specific layer and the second independent task-specific layer is the shared feature, and the output is the predicted friction loss coefficient and the predicted pipe deviation coefficient .

[0036] In a preferred embodiment, the batch normalization layer of one-dimensional data is used between the shared feature extraction layer, the first independent task-specific layer and the second independent task-specific layer, and the shared feature extraction layer is additionally provided with a step-by-step attenuation random neuron inactivation Dropout.

[0037] In a second aspect, the present disclosure provides a coefficient prediction method, comprising:

[0038] obtaining the bridge span L, the bridge height H, the height distribution of the prestressed tendon at the support point section position point on the beam height , the mid-span deflection of the beam under different prestress loss conditions , the mid-span cross-sectional area and the mid-span cross-sectional centroid of the bridge prestressed beam to be predicted.

[0039] The coefficient prediction model constructed by the construction method of the coefficient prediction model of the first aspect is used to predict the friction loss coefficient and the pipe deviation coefficient of the bridge prestressed beam.

[0040] In a third aspect, the present disclosure provides a storage medium storing a computer program, which, when executed by a processor, implements the construction method of the coefficient prediction model of the first aspect.

[0041] The construction method of the coefficient prediction model, the coefficient prediction method and the storage medium described above, by using finite element numerical software to model and simulate the tensioning process of the bridge prestressed beam, extract the parameters, friction loss coefficient information and pipe deviation coefficient The information is used to construct a bridge parameter coefficient array, which is divided into a training data set and a verification data set. The training and verification data sets are standardized and tensor data transformed, a data loader is constructed, and a prediction model is designed by integrating a standardizer and a trained prediction model. The model construction method and coefficient prediction method can quickly and efficiently and accurately predict the friction loss coefficient and the pipeline deviation coefficient by considering the cost, only a few easily measured parameters (bridge span L, bridge height H, and the height distribution of the prestressed tendon positioning point on the beam height at the fulcrum section position , mid-span deflection , mid-span cross-sectional area , and mid-span cross-sectional centroid ) are needed. The model construction method and coefficient prediction method have a wide range of applications and are beneficial to the promotion of the model because the parameters are easy to obtain, which reduces the prediction difficulty of the model application. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 The flowchart of the model construction method for predicting the coefficient in the present disclosure is shown.

[0043] Figure 2 The heat map of the importance of each input feature to the prediction result of the MLP regression model for the friction loss coefficient in the present disclosure is shown.

[0044] Figure 3 The heat map of the importance of each input feature to the prediction result of the MLP regression model for the pipeline deviation coefficient in the present disclosure is shown.

[0045] Figure 4 The diagram of the training loss and the validation loss of different training rounds in the present disclosure is shown.

[0046] Figure 5 The learning rate scheduling diagram of different training rounds in the present disclosure is shown.

[0047] Figure 6 The gradient norm example diagram in the present disclosure is shown.

[0048] Figure 7 The final gradient distribution diagram in the present disclosure is shown.

[0049] Figure 8 The prediction error distribution histogram of the friction loss coefficient in the present disclosure is shown.

[0050] Figure 9 The prediction error distribution histogram of the pipeline deviation coefficient in the present disclosure is shown. ​DETAILED DESCRIPTION

[0051] The technical solutions of the present disclosure will be described in detail below with reference to the drawings and preferred embodiments.

[0052] Referring to Figure 1 A method for constructing a coefficient prediction model, comprising the following steps:

[0053] Step 1, using finite element numerical software to model the bridge prestressed beam and simulate the tensioning process, extracting the parameters of the bridge prestressed beam, the friction loss coefficient Information and pipeline deviation coefficient Information, constructing a bridge parameter coefficient array; the parameters include bridge span L, bridge height H, height distribution of prestressed tendon at fulcrum section position point on beam height , deflection of beam span under different prestressed loss conditions , cross-section area of span And the centroid of the cross-section of the span ;

[0054] Step 2, dividing the bridge parameter coefficient array into training data set and validation data set, and performing data standardization and tensor data conversion on the training data set and the validation data set in turn, and constructing a data loader;

[0055] Step 3, constructing a fully connected multi-layer multi-task neural network based on (activation function) and (activation function) as a prediction model for predicting the friction loss coefficient And pipeline deviation coefficient , wherein the fully connected multi-layer multi-task neural network is provided with a standardizer, a forward propagation function, a loss function, a learning rate scheduler, an optimizer;

[0056] Step 4, defining training function, validation function and training process monitoring function, based on the fully connected multi-layer multi-task neural network and the data loader, performing model training to obtain the trained prediction model for predicting the friction loss coefficient And pipeline deviation coefficient , encapsulating the prediction function, integrating the standardizer and the trained prediction model, providing an interactive input interface, and forming a prediction system.

[0057] The method for constructing the coefficient prediction model will be described in detail below.

[0058] Step 1, using finite element numerical software to model the bridge prestressed beam and simulate the tensioning process, extracting the parameters of the bridge prestressed beam, the friction loss coefficient information and pipe deviation coefficient information, constructing bridge parameter coefficient array, analyzing the importance of each parameter in the bridge parameter coefficient array to the MLP regression model predicting the friction loss coefficient and predicting the pipe deviation coefficient ; the parameters of the bridge prestressed beam include bridge span L, bridge height H, height distribution of prestressed tendon positioning point on the height of the support point section , and mid-span deflection under different prestress loss conditions , mid-span cross-sectional area and mid-span cross-sectional centroid .

[0059] It can be understood that the bridge parameter coefficient array includes friction loss coefficient information, pipe deviation coefficient information, bridge span L, bridge height H, height distribution of prestressed tendon positioning point on the height of the support point section , and mid-span deflection under different prestress loss conditions , mid-span cross-sectional area and mid-span cross-sectional centroid .

[0060] The finite element model is obtained by using the finite element numerical software ANSYS MECHANICAL ENTERPRISE 19.0 to model the prestressed beam. In order to strengthen the universality of model interpretation, different span combinations of bridge span L and bridge height H are traversed, the height distribution of prestressed tendon positioning point on the height of the support point section , the friction loss coefficient information and the pipe deviation coefficient information are traversed. At the same time, in order to facilitate parameter measurement in actual engineering and reference in design stage, the mid-span deflection , mid-span cross-sectional area and mid-span cross-sectional centroid under different prestress loss conditions are selected and extracted after simulation calculation of the finite element model. After establishing the regular expression of the above data in the corresponding result file format, the bridge parameter coefficient array is constructed, that is, after establishing the regular expression of the extracted parameters in the file format, the parameters are extracted to The array (a core data structure for Python scientific computing) is temporarily stored, resulting in an array of bridge parameter coefficients. Warnings for empty files / non-matching data and data distribution checks are added, specifically including outputting the minimum and maximum value ranges, mean range, and distribution based on the bridge parameter coefficient array, to perform a preliminary check on the extracted data and ensure its completeness and validity. After establishing the bridge parameter coefficient array, the feature data (i.e., parameters, input features of the MLP regression model) in this array are established with respect to the friction loss coefficient. Feature importance analysis for predicting pipeline deviation coefficients The importance analysis of data features is used to enhance model interpretability, increase model confidence, and guide model improvement, debugging, and data collection.

[0061] It is understandable that the bridge span L, bridge height H, and height distribution are mentioned. Beam mid-span deflection Mid-span cross-sectional area With the centroid of the mid-span section All of these belong to the original features.

[0062] In this embodiment, before performing feature importance analysis, because different data have different dimensions, and the MLP network architecture is sensitive to the scale of the input features when calculating their mutual importance and influence, directly analyzing the original data will produce large calculation errors and may lead to convergence difficulties. Therefore, a standardization method is used to unify data with different dimensions to the same range. After standardization, a simple MLP regression model based on a neural network is established, using different dimensions from different layers in the subsequent complete model. After training the MLP regression model, the importance of features and labels is calculated, and the corresponding importance is determined by the degree of performance degradation when the original order is disrupted. The repeatability value is set to 10, the importance value is set to the mean, and the random seed is 42. The standardization functions involved are as follows:

[0063] ;

[0064] in: These are the standardized feature values; The value of a certain original feature; for The mean of the original features; This represents the standard deviation of the original features. This is understandable. The values ​​of bridge span L, bridge height H, and the height distribution of prestressing tendons at the support section locations along the beam height are given. The value of , and the mid-span deflection of the beam under different prestress loss conditions. Values, mid-span cross-sectional area The value or centroid of the mid-span section value.

[0065] The MLP regression model is a model for predicting the friction loss coefficient , the pipe deviation coefficient . The neural network structure of the MLP regression model is a single hidden layer multi-layer perceptron, and the forward propagation of the single hidden layer MLP is as follows:

[0066] ;

[0067] wherein: is the output of the single hidden layer, is the input of the single hidden layer, i.e. , is the weight matrix of , is the corresponding bias vector of , is the activation function , is the activation function argument.

[0068] The transmission from the hidden layer to the output layer is as follows:

[0069] ;

[0070] wherein: is the output value of the output layer, i.e. the predicted value of the target variable in the MLP network, is the weight matrix of , is the corresponding bias vector of .

[0071] The calculation formula of the importance is as follows:

[0072] ;

[0073] wherein: denotes the number of the original feature, i.e. the number of the data set of the original feature, is the data set of the th original feature the importance value of the MLP regression model prediction result, used to measure / express the importance of the data set of the th original feature to the MLP regression model prediction result, is the performance value (such as score or MSE index, etc.) of the MLP regression model on the original data (unshuffled data), is the performance value after perturbation, specifically, the performance value of the MLP regression model on the data set of the Dataset of original features The perturbation dataset generated after shuffling the order (i.e., disrupting its relationship with the target) The MLP regression model is based on this perturbation dataset. The calculated performance values ​​after the disturbance.

[0074] For example, the baseline performance of the MLP regression model on the original data is 2500. Now, on the dataset with the original features... Dataset with original features Randomly shuffle each dataset and use the shuffled dataset. and The MLP regression model is re-evaluated, and this process is repeated multiple times. The difference between the original baseline performance and the new evaluation performance value is taken, and the average of the evaluation results in each round is calculated. Finally, the result is obtained regarding... The importance level is 2450, regarding An importance score of 3 indicates that in disrupting... The significant drop in performance of the MLP regression model afterward indicates that it is crucial to the performance of the MLP regression model and disrupts [the system / mechanism]. The performance of the MLP regression model remained essentially unchanged afterward, indicating that it contributed virtually nothing to the performance of the MLP regression model. Based on the above, the heatmap of the specific feature importance ranking results is as follows: Figure 2 and Figure 3 As shown, the MLP regression model is an MLP regression model with the ReLU activation function. Figure 2 and Figure 3 The values ​​are presented in descending order of importance. Figure 2 and Figure 3 As can be seen, the input features analyzed in this embodiment are all robust enough, there are no redundant features, and there is no problem that a certain input feature is too important, which would require the creation of new features related to the feature.

[0075] Step 2: Divide the bridge parameter coefficient array into a training dataset and a validation dataset. Perform data standardization and tensor data transformation on both the training dataset and the validation dataset in sequence to build a data loader.

[0076] (1) Dataset partitioning: To avoid inflated evaluation results due to potential data leakage during training, the dataset is partitioned as follows: Within the library (open-source machine learning libraries in the Python ecosystem) Introduced in China Dataset partitioning function, defining the proportion of the test set. A random seed of 42 is used to proportionally divide the original dataset.

[0077] (2) Data standardization: as in step S101, the optimization algorithm of MLP (such as gradient descent) converges slowly on non-standardized data, and even has problems such as non-convergence. In the training process involving gradient calculation and gradient transmission such as forward propagation and back propagation, too large a difference in the scale of input data may lead to possible gradient disappearance or gradient explosion, the former of which causes the gradient of some neurons to approach 0, and the weights are almost not updated; and the latter causes the gradient of some neurons to be extremely large, resulting in drastic fluctuations in the weights. At the same time, under certain conditions, the numerical range of some features is much larger than that of other features, which may lead the model to rely too much on and thus cause the training result to overfit. Based on the above, the same standardization is selected to scale the original data to ensure dimensional consistency, accelerate model learning iteration convergence, balance gradient update, avoid activation function saturation, and to some extent improve the generalization ability of the model itself.

[0078] (3) Tensor conversion: the multi-task neural network architecture built in the embodiments of the present disclosure is based on an open-source deep learning framework, and the operation logic of the model itself such as matrix multiplication or gradient calculation is based on tensor rather than array. In order to be compatible with the model framework, improve the GPU computing efficiency of model learning, and provide differential support for back propagation itself, the standardized array is converted into a tensor. Specifically, the array after data standardization is converted into a tensor, that is, the bridge parameter coefficient array is an array, and when the bridge parameter coefficient array is divided into a training data set and a validation data set, the training data set and the validation data set are also arrays.

[0079] (4) Building a data loader: the data loader is used for shuffling and batch processing of the training data set (batch processing is to load a specified number of samples during training). The original input data involved in the embodiments of the present disclosure is obtained through four nested loops, which belongs to a large data set. If it is loaded at one time, it will greatly occupy the operation memory and even overload the computer. Therefore, two functions, and are introduced from the data library under the utils module of the torch library, the function is used to combine the tensors after the above processing to obtain a tensor array and make it correctly correspond, so that each individual element in the data set can be in the right order, rather than in a disordered manner, so as to facilitate the calculation and processing of the function. ​​​​The function is used to define the processing batch size for the training data set and the validation data set, and to shuffle the training data set to ensure that the MLP regression model learns the result of the data characteristics and distribution rules rather than the data itself. That is, after the data standardization and tensor data conversion of the training data set and the validation data set, the step of shuffling the training data set is also included, specifically, the function is used to shuffle the training data set.

[0080] Step 3, constructing a full connection multi-layer multi-task neural network based on activation function and activation function as a prediction model for predicting the friction loss coefficient and the pipe deviation coefficient , wherein the full connection multi-layer multi-task neural network is provided with a standardizer, a forward propagation function, a loss function, a learning rate scheduler, and an optimizer.

[0081] Specifically, the full connection multi-layer multi-task neural network includes a shared feature extraction layer, a first independent task specific layer and a second independent task specific layer, wherein the shared feature extraction layer, the first independent task specific layer and the second independent task specific layer are each provided with a standardizer, the input of the shared feature extraction layer is the parameter, and the output is the extracted shared feature, the input of the first independent task specific layer and the second independent task specific layer is the shared feature, and the output is the predicted friction loss coefficient and the predicted pipe deviation coefficient in one-to-one correspondence.

[0082] In this step, a full connection multi-layer multi-task neural network based on a double-coupled activation function of and is constructed, that is, an MLP regression model is constructed, a forward propagation function of multi-task is defined, and a loss function , a related optimizer and a related learning rate scheduling strategy are introduced. Furthermore, the model is also optimized by combining batch normalization and Dropout technology.

[0083] For different prediction parameters in the embodiments of the present disclosure, a multi-dimensional shared function is defined for the feature extraction layer, and batch normalization and multi-layer decreasing deactivation are introduced to enhance the training stability and improve the avoidance of overfitting / underfitting phenomenon. After the corresponding specific layer of the independent task accepts the forward shared bottom layer feature, it independently captures different parameter rules. A splicing type forward propagation function for multi-task is defined, and a related loss function is defined in combination with the task form, calculation cost, data form and calculation efficiency , related optimizer and related learning rate scheduling strategy . Based on the above, the complete neural network model is obtained, which includes a shared layer (i.e., a shared feature extraction layer), an independent layer (an independent task-specific layer), a splicing layer (a multi-task splicing forward propagation), model initialization, a loss function, a training optimizer, and a learning rate scheduling strategy. It can be understood that the independent layer includes a first independent layer and a second independent layer.

[0084] Creating an organizational order in the network layer Ensure the layer propagation direction, use 512~64 progressive dimension reduction on the whole network structure, among which the shared feature extraction layer has a dimension of 512~256 and is attached with a step-by-step decay random neuron inactivation , and the independent task-specific layer has a dimension of 128~64. Batch normalization (the batch normalization layer for one-dimensional data) is used in each layer of the shared feature extraction layer and the independent task-specific layer to alleviate internal covariate shift while accelerating convergence. On the activation function, the activation function is introduced for the shared feature extraction layer to alleviate and prevent possible neuron death when processing high-level general features, provide smooth gradient processing to improve the alleviation of gradient explosion and implicitly suppress overfitting; the activation function is introduced for the independent task-specific layer to provide moderate sparsity and alleviate possible gradient vanishing in the post-training phase, quickly fit the independent task-specific pattern, and complement the hard activation and soft activation of its own to better adapt to complex functions while improving fitting efficiency. In the subsequent forward propagation function definition, the shared feature extraction layer transmits the incoming feature data, the independent task-specific layer transmits the data from the last layer of the shared layer, and the cat function in the library is called to splice the multi-task prediction results into a single tensor for subsequent loss calculation, i.e., the splicing layer splices the results of all independent task-specific layers. In the hyperparameter tuning part, the mean squared error loss function suitable for continuous value prediction scenarios in regression tasks is introduced; the optimizer with more close-to-original L2 regularization and decoupled weight decay is introduced, and the initial learning rate is defined as 0.001, and the decay coefficient is ; the learning rate scheduling strategy is introduced, the specified mode min for the loss monitoring index is 5, the iteration coefficient is 0.5, and the lower limit of the learning rate is . The linear transformation involved is as follows:

[0085] ;

[0086] where: ​Indicates the number of the linear layer; For the first Each n.Linear layer (linear layer) outputs a linear output. For the first Weight matrices for n n.Linear layers; For the first The activation output of an nn.Linear layer network ( ); For the first Bias vectors for each nn.Linear layer.

[0087] Batch standardization is as follows:

[0088] ;

[0089] in: express Standardized output; Indicates the first Each n.Linear layer inputs activation values; Indicates the first The final output after batch normalization of each nn.Linear layer; This is the average value of the current batch. This represents the variance of the current batch. To ensure stable numerical values ​​in batches (to prevent division by zero), most values ​​are taken by default. ; To train learnable scaling and offset parameters.

[0090] The activation function for a specific layer in an independent task is The activation function of the shared feature extraction layer is .

[0091] as follows:

[0092] ;

[0093] in, express Activation function input value, express Activation function express Activation function.

[0094] as follows:

[0095] ;

[0096] in, express Activation function input value, express Activation function.

[0097] The following applies only during training; verification and testing will not:

[0098] ;

[0099] in: For the first n.Linear layers Output value; For the first Input values ​​for an nn.Linear layer; The probability of discarding is, i.e. The value can range from 0.1 to 0.5 depending on the specific requirements.

[0100] The loss function is as follows:

[0101] ;

[0102] in: Indicates the training sample number, indicating the first training sample. One training sample; This represents the total number of training samples. For the model to the first Predicted values ​​for each training sample. For the first The true value of each training sample. for The numerical value of the loss function.

[0103] Regarding the merging of multiple tasks in this network model, there are ,in, This represents the hyperparameter balancing the relative importance of the loss terms. This represents the loss function with weighted penalty terms. Represents the total loss function. express The loss value calculated by the loss function.

[0104] The optimizer is as follows:

[0105] ;

[0106] in, and Indicates the time step, i.e., the number of iterations; Indicates time step That is, the model parameters after one update, which means the model parameters after iterative optimization; This indicates the model parameters that need to be optimized, such as weights or biases. The learning rate; Represents the numerically stable term; This represents the first-order moment estimate of the gradient after bias correction, at time step... The obtained first-order gradient moment estimate after bias correction; For the second-order moment estimate of the gradient after bias correction, the time step is... The obtained second-order gradient moment estimate after bias correction; This is the weight decay coefficient.

[0107] The learning rate scheduler is as follows:

[0108] ;

[0109] in: This represents the learning rate adjusted by the learning rate scheduler. Indicates the current learning rate; For attenuation parameters; This is the lower bound of the learning rate; the scheduler's scheduling strategy itself is triggered by verifying the loss at... (Patience value) did not decrease within the round.

[0110] In summary, with the help of... When the loss function evaluates and penalizes the error of the regression task, The optimizer intervention ensures the suppression of gradient oscillations and overfitting when penalizing bias values ​​during training. The learning rate scheduler also ensures that training is performed when the gradient factor is... This reduces the likelihood of escaping local optima and allows for fine-tuning of hyperparameters. Now, suppose that a single, large gradient exists during the initial training phase for both tasks. The optimizer will intervene and automatically lower the learning rate for a specific period; if the loss value drops to a stable range in a certain epoch and continues to fluctuate, it will continue for a period of time (times / rounds) after the hyperparameter patience. The learning rate scheduler will intervene to reduce the update learning rate to avoid skipping the optimal solution, and will continue to monitor for stagnation of the loss value. loss function Optimizer and The synergistic effect of the learning rate scheduler, the learning rate scheduler, and the learning rate scheduler ensures adaptive optimization and gradient stability while establishing a dynamic parameter tuning and scheduling mechanism, reducing the cost of model operation and debugging, improving the model's generalization ability, increasing convergence computation efficiency, and jointly ensuring training stability.

[0111] Step 4, define training function, validation function and training process monitoring function, based on the full connection multilayer multitask neural network and the data loader, model training is carried out, and the trained prediction model for predicting friction loss coefficient And pipe deviation coefficient The prediction function is encapsulated, the standardizer and the trained prediction model are integrated, the interactive input interface is provided, and the prediction system is formed.

[0112] Step 4.1, model training and validation. Based on the full connection multilayer multitask network structure, related loss function, related optimizer and learning rate scheduling strategy defined in step 3, the training data set and validation data set obtained in step 2 are imported, the training based on loss value is carried out, and the training best model and related standardizer (corresponding to the standardization in the above) are saved, and the training process monitoring is visualized after early stopping or after the training is completed. The specific training process index monitoring diagram is shown in Figures 4 to 7 , Figure 7 The blue in the middle represents the final gradient distribution of all weights in the parameters of Figure 6 The orange represents the final gradient distribution of all biases in the parameters of Figure 6 .

[0113] After importing the related dependent library and receiving the processed training data set and validation data set in steps 2 and 3, data loader, full connection multilayer multitask neural network, related proprietary weight initialization, loss function, model learning optimizer and learning rate scheduling strategy, before training function and validation function, define training monitoring class and specify history label as training loss value, validation loss value, learning rate change, gradient norm change and gradient distribution to save each round of training index and gradient information, etc. for drawing double loss curve, learning rate change curve, gradient L2 norm change curve and final training epoch gradient distribution histogram.

[0114] For the training function, specify the neural network training mode and initialize the training loss value and process monitoring history label, and then loop forward propagation, training loss calculation, back propagation, dynamic gradient clipping and loss accumulation calculation. The loss function And the optimizer Have been explained in the previous step 3, the dynamic gradient clipping ( Library Method) is as follows:

[0115]

[0116] Where: The clipped gradient vector is The original gradient vector is is the L2 norm of the gradient, i.e. the length of the gradient vector; is the number of training steps (iterations); 3.0 is the initial given manual parameter clipping threshold upper limit; 1.0 + 0.05 is the dynamic threshold lower limit.

[0117] For the validation function, the validation loss is initialized after the neural network evaluation mode is specified, and the gradients and parameter updates are disabled for the model to save memory usage and speed up the calculation speed in the performance evaluation link. The average validation loss is returned.

[0118] For the main training loop, the total number of training rounds epochs = 200 is given, the best loss and training process monitor are initialized, and the returned values of the training loss and validation loss are called in the loop. training function and validation function, and because The learning rate scheduling strategy is to adaptively adjust the learning rate based on the validation set index, which is called at the end of each epoch to evaluate the validation loss state and decide whether to adjust the learning rate. After calling the training process monitoring function to record the current training process, the validation loss is compared with the historical best loss to decide whether to early stop. And after the final training is completed (epochs are completed or early stop jumps out), the visualize function is called to visualize the training process indicators, save the visualization results, and serialize the standardizer for subsequent interactive calls. For the MLP and , the back propagation involved is as follows:

[0119] Output layer gradient:

[0120] ;

[0121] ;

[0122] Hidden layer gradient:

[0123] .

[0124] wherein, represents the true label value corresponding to the sample.

[0125] In summary, after the network accepts the parameters, it is forward propagated to the linear transformation layer and the activation function hidden layer, which is multi-dimensional decreasing and sequentially inactivated by neurons, and outputs multi-task splicing. From the above, the back propagation process is entered, the specified loss function is called to calculate the output layer gradient and hidden layer gradient in reverse, and the new weights and new biases are obtained after updating by the chain rule. The synergistic effect ensures the simplicity and efficiency of the code while maintaining the stability of the training and the convergence speed. If the existing original MLP transmission ​For a 10-dimensional feature matrix of the original feature matrix within the incoming flow before forward propagation), the weights and biases in the forward propagation flow are initialized as the corresponding dimension matrix, and the output after the hidden layer activation function is = The final forward propagation output is wherein represents the first element in the weight matrix , represents the second element in the weight matrix , represents the output value of the first element in the vector , i.e., the first hidden layer neuron, and is set to 3.1 for ease of understanding , represents the output value of the second element in the vector , i.e., the second hidden layer neuron. Let it be 1.75 and set the true label value = 2.0, and proceed to the loss gradient calculation in the backpropagation , and are updated as , and backpropagated to the hidden layer to update and .

[0126] Step 4.2, prediction and evaluation: use the trained prediction model to make predictions, restore the data dimension by inverse normalization, and calculate evaluation indicators to evaluate the prediction model. Import the data standardization and tensor data transformation after data standardization and tensor data transformation, call the prediction model and pass in the tensor data for prediction. After converting the prediction results to the original dimension scale by inverse normalization, calculate the score, mean absolute error (MAE) index, and root mean square error (RMSE) index for the multi-task prediction results to quantify the prediction performance, and generate a prediction error distribution histogram for intuitive display of the prediction effect. Define a prediction function and encapsulate it, which functions to accept original geometric parameter input, automatically complete the entire process of standardization conversion, model prediction, and result inverse normalization, and return the final multi-objective prediction value. The specific prediction error distribution histogram is shown in Figure 8 and Figure 9 .

[0127] Import the predefined multi-task neural network model, including the loss function, training optimizer, and learning rate scheduling strategy definition part; pre-encapsulated feature data packages of the training set and validation set after standardization and tensorization; inverse normalization flattening function to adapt the output and restore the dimension to perform prediction. Merge and encapsulate the prediction process and input interface to define a prediction function for easy subsequent new prediction calls. Import function, function to calculate evaluation metrics score, MAE index and RMSE index, are calculated from import from the library sub-library to generate the prediction error distribution histogram. The inverse normalization involved is as follows:

[0128] ’;

[0129] where: is the original dimension data of the original label, that is, the data after the standardized data is restored to the original scale; standardized dimension data; is the standard deviation calculated in the training stage; is the mean value calculated in the training stage.

[0130] The score is as follows:

[0131] ;

[0132] where, denotes the true value, denotes the mean value of the true value, denotes the predicted value.

[0133] The MAE index is as follows:

[0134] ;

[0135] where, denotes the mean absolute error, denotes the total number of samples.

[0136] The RMSE index is as follows:

[0137] ;

[0138] where, denotes the root mean square error.

[0139] Step 4.3, system integration: integrate the standardizer and the trained prediction model, provide an interactive input interface, and form a prediction system.

[0140] Pathological call is made on the pre-trained model (.pth format file) and standardizer (.pkl format file) saved in the previous step, and the above prediction function and user input are integrated to realize a multi-objective prediction system integration of the friction loss coefficient and the pipe deviation coefficient.

[0141] The machine learning framework dependent library, the numerical calculation library, the file loading library and the self-owned model definition are imported, encapsulated into the resource loading function and specified The standardizer and the pre-training model path are used to ensure that the learning logic and the data distribution are consistent with the training process, and the evaluation mode is enabled. In the prediction function, the resource loading function is called to pass the function parameters, the interactive label when accepting user input is defined, the prediction function is called to predict the task target and return the prediction result. Compared with integrating the whole program into the prediction module, the above modular integration hides the preprocessing part corresponding to model loading and data processing, decouples the loading function part and the prediction function part for maintenance and possible expansion, adopts a path-based storage for the model and the standardizer based on lightweight deployment logic, ensures that the target prediction can be directly performed by the historical best model without repeated learning and training, reduces the memory occupation and the calculation cost, defines a clear interactive input interface, makes the whole use and result output clear and easy to read, optimizes the model use efficiency, and reduces the prediction process use difficulty.

[0142] The present disclosure provides a coefficient prediction model construction system, comprising:

[0143] A modeling and parameter acquisition module is used to model the bridge prestressed beam by using finite element numerical software and simulate the tensioning process, extract the parameters of the bridge prestressed beam, the friction loss coefficient Information and pipeline deviation coefficient Information, construct a bridge parameter coefficient array; the parameters of the bridge prestressed beam include bridge span L, bridge height H, height distribution of prestressed tendon positioning point at support section position on beam height , deflection of beam span under different prestress loss conditions , cross-section area of span And the centroid of the cross-section of the span ;

[0144] A data set processing module is used to divide the bridge parameter coefficient array into a training data set and a verification data set, and perform data standardization and tensor data conversion on the training data set and the verification data set in turn;

[0145] A construction module is used to construct a data loader; a fully connected multilayer multitask neural network based on And As a prediction model for predicting the friction loss coefficient And the pipeline deviation coefficient , the fully connected multilayer multitask neural network is provided with a standardizer, a forward propagation function, A loss function, A learning rate scheduler, An optimizer;

[0146] A definition and training module is configured to define a training function, a verification function, and a training process monitoring function, based on the full-connection multi-layer multi-task neural network and the data loader, to perform model training to obtain a trained prediction model, to encapsulate a prediction function, and to integrate a standardizer and the trained prediction model to provide an interactive input interface to form a prediction system.

[0147] The coefficient prediction model construction system can be implemented by referring to the coefficient prediction model construction method in any of the above embodiments, and the specific implementation steps will not be described again.

[0148] The disclosure also provides a computer-readable storage medium comprising instructions that, when executed on a computer, cause the computer to perform the steps of the coefficient prediction model construction method described in any of the above embodiments.

[0149] The method according to the disclosure can implement a computer program product comprising a computer program or instructions that, when executed by a processor, implement the coefficient prediction model construction method.

[0150] The disclosure provides a coefficient prediction method, comprising:

[0151] obtaining the bridge span L, the bridge height H, the height distribution of the positioning point of the prestressed tendon at the fulcrum section position on the beam height of the bridge prestressed beam to be predicted , the mid-span deflection of the beam under different prestress loss conditions , the mid-span cross-sectional area , and the mid-span cross-sectional centroid ;

[0152] The coefficient prediction model constructed by the coefficient prediction model construction method (preferably using the prediction system) is used to predict the friction loss coefficient of the bridge prestressed beam and the pipe deviation coefficient .

[0153] The disclosure also provides a coefficient prediction system, comprising:

[0154] A data acquisition module is configured to acquire the bridge span L, the bridge height H, the height distribution of the positioning point of the prestressed tendon at the fulcrum section position on the beam height of the bridge prestressed beam to be predicted , the mid-span deflection of the beam under different prestress loss conditions , the mid-span cross-sectional area , and the mid-span cross-sectional centroid ;

[0155] a prediction module configured to predict the friction loss coefficient of the bridge prestressed beam by using the coefficient prediction model constructed by the construction method of the coefficient prediction model and a pipe deviation coefficient .

[0156] The method according to the present disclosure can realize an electronic device, which comprises a memory, one or more processors, and one or more programs stored in the memory and configured to be executed by the one or more processors, the one or more programs comprising instructions for performing a coefficient prediction method according to any one of the above embodiments.

[0157] It should be noted that in the above embodiments, the description of each embodiment has its own emphasis, and the parts not described in detail in a certain embodiment can be referred to the related description of other embodiments.

[0158] The construction method of the coefficient prediction model, the coefficient prediction method and the storage medium provided by the present disclosure have the following effects: based on the bridge span L, the bridge height H, the height distribution of the positioning point of the prestressed tendon at the fulcrum section position on the beam height , the mid-span deflection of the beam under different prestress loss conditions , the mid-span section area and the mid-span section centroid These parameters are easy to obtain, and since the parameters are easy to obtain, the prediction difficulty of the model when applied is reduced, thereby the model has a wide range of applications and is beneficial to the promotion of the model; by fusing finite element simulation and deep learning technology, through the steps of data preprocessing, neural network construction, model training and verification, prediction evaluation and model system integration, through the analysis of the multi-working condition data set, the friction loss coefficient and the pipe deviation coefficient The data set of the present disclosure can reflect the construction differences in specific projects based on the parameters of various bridge prestressed beams, compared with the traditional specification simplification method. Compared with the traditional theoretical formula method, the empirical coefficient method and the simulation method, the present disclosure can adapt to the nonlinear factors in the engineering practice, greatly reduce the calculation and prediction error, and significantly improve the calculation efficiency and accuracy. The prediction model can be self-adjusted to a certain extent for different spans, different prestressed tendon arrangements and different condition cases, making up for the inapplicability of the empirical coefficient method and the like in non-standard design of new materials or special process conditions, and enhancing the engineering applicability. The modular integrated calling system of the present disclosure saves more than 90% of the modeling and analysis calculation time compared with the traditional numerical iteration simulation, and does not need to repeat modeling, only needs a few real-time measurable parameters, and supports process and result visualization prediction system, which significantly shortens the design cycle and detection time of the application related technology engineering, and greatly improves the overall construction efficiency. The present disclosure does not need to use related sensors for field calibration, and saves the reusable pre-trained model, reduces the hardware investment, and saves the software calculation resource cost. The present disclosure can simultaneously consider the project duration and construction efficiency, time benefit, calculation accuracy and calculation cost.

[0159] The scientific optimization decision of the present disclosure provides a plurality of enhanced error quantification indexes and corresponding visual analysis to assist in judging the prediction reliability, provides data support for subsequent secondary tensioning or design stage over-tensioning ratio and prestressed duct alignment optimization, controls and reduces the risk of prestress loss over-limit from the source, and to a certain extent, throttles the material usage to reduce the engineering cost, and has good application prospect and economic benefit.

[0160] The technical features of the above-described embodiments can be combined in any manner. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described, but as long as the combinations of the technical features do not exist contradictory, they should be considered as the scope of the present disclosure.

[0161] The above-described embodiments only express several implementation manners of the present disclosure, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be noted that for ordinary skilled persons in the art, without departing from the concept of the present disclosure, a number of modifications and improvements can be made, which are within the scope of the present disclosure. Therefore, the protection scope of the present disclosure patent should be subject to the appended claims.

Claims

1. A method for constructing a coefficient prediction model, characterized in that, Includes the following steps: Step 1: Model the prestressed beam of the bridge using finite element method (FEM) software and simulate the tensioning process to extract the parameters and friction loss coefficient of the prestressed beam. Information and pipeline deviation coefficient Information is used to construct a bridge parameter coefficient array; the parameters of the prestressed beam include the bridge span L, bridge height H, and the height distribution of the prestressing tendons at the support section positions along the beam height. It also includes the mid-span deflection of beams under different prestress loss conditions. Mid-span cross-sectional area With the centroid of the mid-span section ; Step 2: Divide the bridge parameter coefficient array into a training dataset and a validation dataset. Perform data standardization and tensor data transformation on both the training dataset and the validation dataset in sequence, and build a data loader. Step 3, build based on and A fully connected multilayer multitasking neural network with activation function is used to predict friction loss coefficients. and pipeline deviation coefficient The prediction model, wherein the fully connected multilayer multitasking neural network includes a normalizer, a forward propagation function, and loss function Learning rate scheduler Optimizer; Step 4: Define the training function, validation function, and training process monitoring function. Based on the fully connected multi-layer multi-task neural network and the data loader, train the prediction model to obtain the trained prediction model. Encapsulate the prediction function, integrate the normalizer and the trained prediction model, provide an interactive input interface, and form a prediction system.

2. The method for constructing a coefficient prediction model according to claim 1, characterized in that, Step 1 includes analyzing how each parameter in the bridge parameter coefficient array affects the MLP regression model's prediction of the friction loss coefficient. Importance and Predictive Pipe Deviation Coefficient The importance of.

3. The method for constructing a coefficient prediction model according to claim 1, characterized in that, The steps for constructing the bridge parameter coefficient array include: creating a regular expression in file format for the extracted parameters, and constructing the bridge parameter coefficient array based on the regular expression.

4. The method for constructing a coefficient prediction model according to claim 1, characterized in that, The bridge parameter coefficient array is as follows: Array, the data is standardized as Standardization, the tensor data is transformed into a standardized form. Array to Tensor.

5. The method for constructing a coefficient prediction model according to claim 1, characterized in that, The The loss function is: ； in: Indicates the training sample number, indicating the first training sample. One training sample; This represents the total number of training samples. For the model to the first Predicted values ​​for each training sample. For the first The true value of each training sample. for The numerical value of the loss function; The total loss function of the prediction model is: ； in, This represents the hyperparameter balancing the relative importance of the loss terms. This represents the loss function with weighted penalty terms. Represents the total loss function; The The optimizer satisfies: ； in, This represents the updated model parameters; Indicates the model parameters that need to be optimized; The learning rate; Represents the numerically stable term; This represents the first-order moment estimate of the gradient after bias correction; This is the second-order moment estimate of the gradient after bias correction; This is the weight decay coefficient; The learning rate scheduler satisfies: ； in: This represents the learning rate adjusted by the learning rate scheduler. Indicates the current learning rate; For attenuation parameters; This is the lower limit of the learning rate; the trigger condition for the scheduling strategy is to verify that the loss has not decreased within the patience value rounds.

6. The method for constructing a coefficient prediction model according to claim 1, characterized in that, Step 4 further includes: using the trained prediction model to make predictions, restoring the data dimensions through inverse standardization, and calculating evaluation indicators to evaluate the prediction model.

7. The method for constructing a coefficient prediction model according to claim 1, characterized in that, The fully connected multi-layer multi-task neural network includes a shared feature extraction layer, a first task-specific layer, and a second task-specific layer. Each of these layers contains a normalizer. The input to the shared feature extraction layer is the parameters, and the output is the extracted shared features. The input to both the first and second task-specific layers is the shared features, and the outputs are the predicted friction loss coefficients. And the predicted pipeline deviation coefficient .

8. The method for constructing a coefficient prediction model according to claim 7, characterized in that, The shared feature extraction layer, the first independent task-specific layer, and the second independent task-specific layer are connected by a batch normalization layer for one-dimensional data. The shared feature extraction layer is supplemented with Dropout, a staggered random neuron deactivation method.

9. A coefficient prediction method, characterized in that, include: Obtain the bridge span L, bridge height H, and height distribution of the prestressed tendons at the support sections along the beam height for the prestressed beam to be predicted. And the mid-span deflection of the beam under different prestress loss conditions. Mid-span cross-sectional area With the centroid of the mid-span section ; The coefficient prediction model constructed using the method described in any one of claims 1-8 predicts the friction loss coefficient of prestressed bridge beams. and pipeline deviation coefficient .

10. A storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for constructing a coefficient prediction model according to any one of claims 1-8.

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