Construction method of coefficient prediction model, coefficient prediction method and storage medium

Abstract

The invention relates to a construction method of a coefficient prediction model, a coefficient prediction method and a storage medium, and the construction method comprises the steps: carrying out the modeling of a bridge prestressed beam through finite element numerical software, simulating a tensioning process, constructing a bridge parameter coefficient array, dividing the bridge parameter coefficient array into a training data set and a verification data set, performing data standardization and tensor data conversion, and constructing a data loader; an AND-based full-connection multi-layer multi-task neural network is constructed, and a standardizing device, a forward propagation function, a loss function, a learning rate scheduler and an optimizer are arranged; and carrying out model training, packaging a prediction function, and integrating a standardizing device and the trained prediction model. The prediction method comprises the step of predicting the friction resistance loss coefficient and the pipeline deviation coefficient according to the prediction model. According to the method and the device, coefficient prediction can be quickly, efficiently and accurately realized by only needing several on-site easy-to-measure 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 The predicted value of 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 eigenvalues; 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 defines the batch size for both the training and validation datasets and shuffles the training dataset to ensure that the MLP regression model learns data features and distribution patterns rather than the data itself. In other words, after standardizing and transforming both the training and validation datasets using tensors, it also includes a step of shuffling the training dataset. Specifically, it utilizes... The function shuffles the training dataset.

[0080] Step 3, build based on Activation function 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;

[0081] Specifically, 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 their corresponding outputs are the predicted friction loss coefficients. And the predicted pipeline deviation coefficient .

[0082] In this step, build based on and A fully connected multilayer multitasking neural network with a bicoupled activation function is constructed, i.e., an MLP regression model is built, defining the forward propagation function for multiple tasks and introducing a loss function. Related optimizers and related learning rate scheduling strategies Furthermore, it combines batch standardization with Dropout technology to optimize the model.

[0083] For different prediction parameters in this embodiment, a multidimensional shared function is defined for the feature extraction layer. Batch standardization is also introduced to enhance training stability and improve overfitting / underfitting. Multi-layer deactivation For individual tasks, a specific layer is defined that receives shared low-level features from the forward pass and then independently captures the patterns of different parameters. A concatenated forward propagation function is defined for multiple tasks, and relevant loss functions are defined considering task format, computational cost, data format, and computational efficiency. Related optimizers Related learning rate scheduling strategies Based on the above, a complete neural network model is obtained, comprising a shared layer (i.e., a shared feature extraction layer), independent layers (task-specific layers), a concatenation layer (multi-task concatenation forward propagation), model initialization, a loss function, a training optimizer, and a learning rate scheduling strategy. It is understood that the independent layers include a first independent layer and a second independent layer.

[0084] Create an organization sequencer in the network layer To ensure the direction of layer propagation, a progressive dimensionality reduction of 512 to 64 is used across the entire network structure, with the shared feature extraction layer having a dimension of 512 to 256 and employing progressively decaying random neuron inactivation. The dimensions of the task-specific layers range from 128 to 64. Both the shared feature extraction layer and the task-specific layers use batch normalization for each layer. (Batch normalization layer for one-dimensional data) to accelerate convergence while mitigating internal covariate bias. An activation function is introduced for the shared feature extraction layer. To mitigate and prevent potential neuron death during high-level general feature processing, provide smooth, gradual gradient processing to improve gradient explosion mitigation and implicitly suppress overfitting; and introduce activation functions for task-specific layers. To provide moderate sparsity and mitigate potential gradient vanishing later in training, it quickly fits task-specific patterns independently and leverages its own hard activation and The soft activation is complemented, making it more adaptable to complex functions while improving fitting efficiency. In the subsequent forward propagation function definition, feature data is passed to the shared feature extraction layer, and data from the last layer of the shared layer is passed to the task-specific layer, and then the function is called... The `cat` function in the library concatenates multi-task prediction results into a single tensor for subsequent loss calculation; that is, the concatenation layer combines the results of all independent task-specific layers. In the hyperparameter tuning section, a mean squared error loss function suitable for continuous value prediction scenarios in regression tasks is introduced. Introducing a decoupled weight decay mechanism that more closely resembles the original L2 regularization. The optimizer is set with an initial learning rate of 0.001 and a decay factor of 1. Introducing a learning rate scheduling strategy For the loss monitoring metric, the specified mode is min, the learning rate decay patience counter is 5, the iteration coefficient is 0.5, and the lower bound of the learning rate is... Involving The linear transformation is as follows:

[0085] ;

[0086] in: 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 nn.Linear layer input 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 The predicted value of 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 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, perform model training to obtain the trained model used to predict friction loss coefficients. and pipeline deviation coefficient The prediction model is encapsulated with prediction functions, and a normalizer and the trained prediction model are integrated to provide an interactive input interface, forming a prediction system.

[0112] Step 4.1, Model Training and Validation. Based on the fully connected multi-layer multi-task network structure, relevant loss function, relevant optimizer, and learning rate scheduling strategy defined in Step 3, import the training and validation datasets obtained in Step 2, perform loss-based training, and simultaneously save the best-performing model and the relevant normalizer (corresponding to the normalization mentioned above). Visualize the training process monitoring after early stopping or after training ends. A specific training process metric monitoring diagram is shown below. Figures 4 to 7 As shown, Figure 7 Medium blue indicates Figure 6 The final gradient distribution common to all weights in the parameters, represented in orange. Figure 6 The final gradient distribution is the common distribution of all biases in the parameters.

[0113] After importing the relevant dependency libraries and receiving the processed training and validation datasets, data loader, fully connected multilayer multitasking neural network, relevant proprietary weight initialization, loss function, model learning optimizer, and learning rate scheduling strategy from steps 2 and 3, a training monitoring class is defined before the training and validation functions. The historical labels are specified as training loss value, validation loss value, learning rate change, gradient norm change, and gradient distribution to save the training metrics and gradient information for each round, which are used to draw the two-way loss curve, learning rate change curve, gradient L2 norm change curve, and the gradient distribution histogram of the final training epoch.

[0114] For the training function, the neural network training mode is specified, and the training loss value and process monitoring history labels are initialized. Then, forward propagation, training loss calculation, back propagation, dynamic gradient clipping, and loss accumulation calculation are performed in a loop. The loss function involved is... With optimizer As explained in step 3 above, dynamic gradient clipping is given here. Inside the library The method is as follows:

[0115]

[0116] in: This is the clipped gradient vector. This is the original gradient vector; This is the L2 norm of the gradient, i.e., the magnitude of the gradient vector; 3 is the number of training steps (iterations); 3.0 is the initial upper limit of the manually set pruning threshold; 1.0 + 0.05 This is the lower limit of the dynamic threshold.

[0117] For the validation function, initialize the validation loss after specifying the neural network evaluation mode. To save memory usage in the performance evaluation stage and speed up computation, disable gradient and parameter updates for the model. Return the average validation loss.

[0118] For the main training loop, given a total training epochs of 200, initialize the optimal loss and training process monitor. Within the loop, call the training and validation functions to obtain return values ​​for the training and validation losses, and then... The learning rate scheduling strategy is based on the validation set metrics, which are adaptively and dynamically adjusted. This is called at the end of each epoch to evaluate the validation loss status and determine whether to adjust the learning rate. After the training process monitoring function records the current training process, the validation loss is compared with the historical best loss to determine whether to stop early. Finally, after the training is completed (epochs finished or early stop), the `visualize` function is called to visualize the various metrics of the training process, save the visualization results, and serialize the normalizer for subsequent interactive calls. The MLP and... (The sentence is incomplete and requires further context to translate accurately.) The backpropagation involved is as follows:

[0119] Output layer gradient:

[0120] ;

[0121] ;

[0122] Hidden layer gradient:

[0123] .

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

[0125] In summary, after the network receives the parameters, they are forwarded to the linear transformation layer and... The activation function in the hidden layer is multidimensionally reduced, and the output is concatenated after successive neuron inactivation. From there, the backpropagation process begins, calling the specified loss function to calculate the gradients of the output and hidden layers. After updating using the chain rule, new weights and biases are obtained. This synergistic effect ensures both code conciseness and efficiency while maintaining training stability and convergence speed. If the existing original MLP is passed... ( If the 10-dimensional feature matrix is ​​the original feature matrix passed into the process before forward propagation, then the weights and biases in the forward propagation process are initialized to the corresponding dimension matrices, and output after passing through the hidden layer activation function. = Then there is a final forward propagation output. ,in, Represents the weight matrix The first element in Represents the weight matrix The second element in Representing vectors The first element is the output value of the first hidden layer neuron. For ease of understanding, this... The value is 3.1. Representing vectors The second element is the output value of the second hidden layer neuron. Let it be 1.75 and set the true label value. =2.0, proceeding to backpropagation with loss gradient calculation Update at this time and like , And backpropagate to the hidden layer to achieve [the desired result]. and Update.

[0126] Step 4.2, Prediction and Evaluation: Prediction is performed using the trained prediction model. Data dimensions are restored through inverse standardization, and evaluation metrics are calculated to assess the prediction model. The standardized and tensor-transformed data are imported, and the prediction model is invoked with tensor data input for prediction. After inverse standardization transforms the prediction results to the original dimensional scale, the metrics are calculated for each multi-task prediction result. Three metrics—prediction score, mean absolute error (MAE) index, and root mean square error (RMSE) index—are used to quantitatively evaluate prediction performance. A histogram of prediction error distribution is also generated to visually represent the prediction results. A prediction function is defined and encapsulated; its function is to accept the original geometric parameters as input, automatically complete the entire process of standardization transformation, model prediction, and inverse standardization of the results, and return the final multi-objective prediction value. The specific prediction error distribution histogram is shown below. Figure 8 and Figure 9 As shown.

[0127] Import a predefined multi-task neural network model, including the loss function, training optimizer, and learning rate scheduling strategy definitions; pre-packaged, standardized and tensorized training and validation set feature data packages; and an inverse standardized flattening function that adapts the output and restores its dimensions for prediction. Merge the prediction process and input interface into a single prediction function for easy invocation of subsequent predictions. function, Functions to calculate evaluation metrics Score, MAE index and RMSE index, by Import from library The sub-library is used to generate a histogram of the prediction error distribution. The inverse standardization involved is as follows:

[0128] ';

[0129] in: This refers to the original dimensional data with the original label, that is, the data after standardization is restored to the original scale. Standardized dimensional data; The standard deviation is calculated for the training phase; This is the mean calculated during the training phase.

[0130] The scores are as follows:

[0131] ;

[0132] in, Represents the actual value. The mean of the true values. This represents the predicted value.

[0133] The MAE index is as follows:

[0134] ;

[0135] in, Indicates the mean absolute error. This represents the total number of samples.

[0136] The RMSE index is as follows:

[0137] ;

[0138] in, This represents the root mean square error.

[0139] Step 4.3, System Integration: Integrate the normalizer and the trained prediction model, provide an interactive input interface, and form a prediction system.

[0140] The pre-trained model (.pth format file) and normalizer (.pkl format file) saved in the previous step are called in a path-based manner. The above are integrated with the prediction function and user input to realize the multi-objective prediction system integration of friction loss coefficient and pipeline deviation coefficient.

[0141] This approach imports machine learning framework dependencies, numerical computation libraries, file loading libraries, and custom model definitions, encapsulating them within a resource loading function. It specifies the paths to the normalizer and pre-trained model to ensure consistency between the learning logic and data distribution and the training process, and enables the evaluation mode. The resource loading function is called within the prediction function to pass function parameters. Interaction labels for accepting user input are defined, and the encapsulated prediction function is called to predict the task objective and return the prediction result. This modular integration, compared to integrating the entire program into the prediction module, hides the preprocessing parts corresponding to model loading and data processing, decouples the loading function from the prediction function for better maintenance and potential expansion, and uses a path-based storage for the model and normalizer that can be directly called and switched based on a lightweight deployment logic. This ensures that each time the application is reused, it can skip multiple repetitive learning and training cycles and directly execute target prediction using the historical best model, reducing memory usage and computational costs. A clear interactive input interface is defined, making the overall usage and result output clear and easy to read. Model usage efficiency is optimized, and the prediction process is made more user-friendly.

[0142] This disclosure provides a system for constructing a coefficient prediction model, including:

[0143] The modeling and parameter acquisition module is used to model bridge prestressed beams and simulate the tensioning process using finite element numerical software, extracting parameters and friction loss coefficients of the bridge prestressed beams. 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 ;

[0144] The dataset processing module is used to divide the bridge parameter coefficient array into a training dataset and a validation dataset, and to perform data standardization and tensor data transformation on both the training dataset and the validation dataset in turn.

[0145] Build modules are used to build data loaders; they are used to build based on... and A fully connected multilayer multitasking neural network was used to predict the friction loss coefficient. 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;

[0146] The definition and training module is used to define training functions, verification functions, and training process monitoring functions. Based on the fully connected multi-layer multi-task neural network and the data loader, it performs model training to obtain the trained prediction model. It is used to encapsulate the prediction function, integrate the normalizer and the trained prediction model, and provide an interactive input interface to form a prediction system.

[0147] In specific implementation, the coefficient prediction model construction system can refer to one of the coefficient prediction model construction methods in any of the above embodiments to construct the prediction model. The specific implementation steps will not be repeated.

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

[0149] According to the method disclosed herein, a computer program product can be implemented, including a computer program or instructions, which, when executed by a processor, implement the method for constructing a coefficient prediction model.

[0150] This disclosure provides a coefficient prediction method, including:

[0151] 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 ;

[0152] The coefficient prediction model constructed using the aforementioned method (preferably employing the aforementioned prediction system) predicts the friction loss coefficient of prestressed bridge beams. and pipeline deviation coefficient .

[0153] This disclosure also provides a coefficient prediction system, including:

[0154] The data acquisition module is used to acquire the bridge span L, bridge height H, and height distribution of the prestressed tendons at the support sections of the prestressed beam to be predicted along the beam height. 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 ;

[0155] The prediction module is used to predict the friction loss coefficient of a prestressed bridge beam using the coefficient prediction model constructed by the aforementioned coefficient prediction model construction method. and pipeline deviation coefficient .

[0156] An electronic device can be implemented according to the method of this disclosure, the electronic device comprising: a memory; one or more processors; one or more programs, wherein the one or more programs are 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 of the above embodiments.

[0157] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0158] The method for constructing a coefficient prediction model, the coefficient prediction method, and the storage medium disclosed herein have the following effect: based on the bridge span L, bridge height H, and the height distribution of the prestressing tendons at the support section positions on 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 These parameters are all readily available, which reduces the prediction difficulty when applying the model, thus broadening its applicability and facilitating its promotion. By integrating finite element simulation and deep learning techniques, and through steps such as data preprocessing, neural network construction, model training and validation, prediction evaluation, and model system integration, this study analyzes multi-condition datasets and utilizes an MLP multi-task architecture to determine the friction loss coefficient in bridge prestressed friction loss. Pipeline deviation coefficient The accuracy of predictions is enhanced. Compared to traditional simplified methods, the dataset in this disclosure is based on parameters of various prestressed beams for bridges, reflecting the construction differences in specific projects. Compared to traditional theoretical formula methods, empirical coefficient methods, and simulation methods, this disclosure can adapt to nonlinear factors in actual engineering, significantly reducing calculation and prediction errors and significantly improving calculation efficiency and accuracy. The prediction model can self-adjust to a certain extent for different spans, different prestressed tendon arrangements, and different working conditions, compensating for the inapplicability of empirical coefficient methods under non-standard designs such as new materials or special process conditions, thus enhancing engineering applicability. The modular integrated calling system of this disclosure saves more than 90% of modeling and analysis calculation time compared to traditional numerical iterative simulation, eliminating the need for repeated modeling. The prediction system, requiring only a few easily measurable parameters and supporting process and result visualization, significantly shortens the design cycle and inspection time for projects applying related technologies, greatly improving overall construction efficiency. This disclosure eliminates the need for relevant sensors used in actual measurement and saves reusable pre-trained models, reducing hardware investment while saving software computing resource costs. This disclosure can simultaneously take into account project schedule and construction efficiency, time efficiency, calculation accuracy, and calculation cost.

[0159] This scientifically optimized decision-making method provides multiple enhanced error quantification indicators and corresponding visualization analysis to assist in judging the reliability of the prediction results. It provides data support for subsequent secondary tensioning or optimization of the over-tensioning ratio and prestressed duct alignment in the design stage. It controls and reduces the risk of excessive prestress loss from the source and saves material usage to a certain extent, thereby reducing engineering costs. It has good application prospects and economic benefits.

[0160] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0161] The embodiments described above are merely illustrative of several implementations of this disclosure, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this disclosure, and these all fall within the protection scope of this disclosure. Therefore, the protection scope of this patent should be determined by 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 The predicted value of 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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