A prestress tension loss value prediction method and system based on machine learning

Abstract

The application belongs to the technical field of machine learning and prestress, and discloses a prestress tension loss value prediction method and system based on machine learning, which comprises the following steps: adopting finite element numerical software to model and simulate prestressed beams under multiple working conditions, extracting prestressed beam working parameters and design parameters, and performing data preprocessing, distribution inspection and feature importance analysis to obtain an initial data set; dividing the initial data set into an initial training data set and an initial test data set and processing them to obtain a processed training data set and a processed test data set; constructing a fully connected multilayer perception neural network model, defining training, verification and monitoring functions, training the fully connected multilayer perception neural network model by using the processed training data set, testing the trained model by using the processed test data set, and obtaining a prediction model; and obtaining real parameters of the prestressed beam, predicting the prestress tension loss value by using the prediction model, and obtaining a prediction result.

Description

Technical Field

[0001] This invention belongs to the fields of machine learning and prestressing technology, specifically relating to a method and system for predicting prestressing release loss values ​​based on machine learning. Background Technology

[0002] Prestressing technology is a key technology in modern concrete structure engineering, widely used in important infrastructure such as long-span bridges, high-rise buildings, industrial plants, railway sleepers, and nuclear power plant containment structures. Its core principle is to pre-tension prestressing tendons (such as steel strands, wires, or threaded steel bars) and transfer this force to the concrete member after anchorage, thus artificially establishing prestress before the structure bears external loads. This prestressing effectively counteracts tensile stresses caused by live loads, wind loads, or seismic actions during the service life, significantly improving the structure's crack resistance, stiffness, and long-term durability. However, during the crucial stage of prestressing construction—the release process (i.e., releasing the tensioning equipment and transferring the tension of the prestressing tendons to the concrete member)—prestress loss inevitably occurs. This loss is mainly caused by the following factors: slippage deformation between the anchorage and the bearing plate, and wedge retraction; elastic compressive deformation, creep, and shrinkage effects of the concrete; stress relaxation of the prestressing tendons; temperature changes; deviations in the tensioning sequence; or frictional losses. These factors are coupled with each other, resulting in significant uncertainty in the final prestress loss value (i.e., the difference between the initial tension and the actual effective prestress).

[0003] In engineering practice, the accurate prediction of prestress loss is directly related to the safety and economy of the structure. If the predicted value is too small, it may lead to insufficient actual prestress, causing structural cracking or excessive deformation; if the predicted value is too large, it will result in material waste or overloading of tensioning equipment. Currently, the industry generally uses the theoretical formulas provided in the specifications for estimation, which are based on elasticity mechanics, classifying losses into two categories: instantaneous losses (such as anchor deformation and elastic compression of concrete) and long-term losses (such as creep, shrinkage, and relaxation), and deriving analytical solutions through simplifying assumptions (such as linear materials and uniform stress distribution). However, in actual engineering, factors such as the non-homogeneity of concrete, spatial compression and temporal axis changes caused by environmental temperature and humidity, and fluctuations in construction technology (such as uneven tensioning rates) all introduce nonlinear effects, causing the predicted results of the specification formulas to deviate from the measured values ​​by 15% to 30%. In response, some studies have attempted to improve the prediction accuracy by introducing correction coefficients or combining finite element numerical simulations, but these methods are still limited by the empirical nature of parameter calibration or the computational complexity. In recent years, with the development of sensor technology and construction informatization, a large amount of multi-source data (such as tension monitoring values, concrete strength time history curves, and environmental temperature and humidity records) in the prestressed construction process has been accumulated, making it possible to develop new data-driven prediction methods such as random forests, support vector machines, and neural networks. However, these methods are mostly applied to single engineering cases and lack cross-project generalization verification.

[0004] Based on the above shortcomings, this invention proposes a hybrid prediction method that integrates finite element simulation and machine learning to address the prestress loss value generated after release in prestressed engineering. By combining generalization of a large number of simulated samples and data-driven nonlinear compensation, the prediction accuracy and model generalization ability are improved. At the same time, relatively easily measurable feature engineering and model interpretation analysis are introduced to provide transparent support for engineering decision-making. Summary of the Invention

[0005] This invention aims to address the shortcomings of existing technologies and provides the following solutions:

[0006] A machine learning-based method for predicting prestress release loss includes the following steps:

[0007] Finite element numerical software was used to model and simulate the prestressed beam under multiple working conditions. The working parameters and design parameters of the prestressed beam were extracted, and data preprocessing, distribution checking and feature importance analysis were performed to obtain the initial dataset.

[0008] The initial dataset is divided into an initial training dataset and an initial test dataset and processed to obtain a processed training dataset and a processed test dataset.

[0009] A fully connected multilayer perceptron neural network model is constructed, training, validation, and monitoring functions are defined, the fully connected multilayer perceptron neural network model is trained using the processed training dataset, and the trained model is tested using the processed test dataset to obtain a prediction model.

[0010] Obtain the actual parameters of the prestressed beam, and based on the actual parameters, use the prediction model to predict the prestress release loss value to obtain the prediction result.

[0011] Preferably, the method for obtaining the initial dataset includes:

[0012] Establish a finite element model and iterate through the dimensions and prestressing tendon height parameters of the prestressed beam;

[0013] The cross-sectional area, centroid, moment of inertia, and deflection characteristics of the prestressed beam under different working conditions are extracted, and the dimensional differences of the extracted parameters are eliminated to obtain preprocessed data.

[0014] The preprocessed data is subjected to data distribution checks, feature linear correlation calculations, and then... n _ repeat The initial dataset is obtained by performing feature importance analysis of MLP using the perturbation method.

[0015] Preferred methods for obtaining the processed training dataset and the processed test dataset include:

[0016] use train _ test _ split The function divides the initial dataset proportionally to obtain the initial training set and the initial test dataset;

[0017] The initial training set and the initial test dataset are standardized to obtain a standardized initial training set and a standardized initial test set.

[0018] The standardized initial training set and the standardized initial test set are subjected to tensor transformation, and then introduced... TensorDataset and DataLoader The transformed training dataset is shuffled to obtain the processed training dataset and the processed test dataset.

[0019] Preferably, the method for obtaining the prediction model includes:

[0020] Construct a fully connected multilayer perceptron neural network model, including: a feature input layer, a hidden layer, and an output layer;

[0021] Definition Combination LeakyReLU Functions and SiLUThe doubly coupled composite activation function and the forward propagation function;

[0022] Introducing the mean squared error loss function MSELoss Optimizer AdamW and dynamic adjustment of learning rate scheduling strategy ReduceLROnPlateau ;

[0023] The hidden layer incorporates batch normalization. BatchNorm1d The fully connected multilayer perceptron neural network model is optimized using a hierarchical non-uniform neuron inactivation technique.

[0024] The optimized fully connected multilayer perceptron neural network model is trained using the processed training dataset, and the trained model is tested using the processed test dataset to obtain the prediction model.

[0025] Preferably, the LeakyReLU The function is:

[0026] ,

[0027] in, max This means taking the maximum of the two values. x This represents the input value of the function. α Indicates the negative slope coefficient;

[0028] The SiLU The function is:

[0029] ,

[0030] in, s express Sigmoid function.

[0031] Preferably, the mean squared error loss function MSELoss for:

[0032] ,

[0033] in, n This represents the total number of samples. i Indicates the first i One sample, Represents the actual value. Indicates the model's predicted value;

[0034] The optimizer AdamW for:

[0035] ,

[0036] in, or Indicates the learning rate. This represents the first moment of the gradient after bias correction. This represents the second moment of the gradient after bias correction. l This represents the weight decay coefficient. ϵ Represents the batch-standardized numerically stable term. i t Indicates the first t Step parameters;

[0037] The dynamic learning rate adjustment scheduling strategy ReduceLROnPlateau for:

[0038] ,

[0039] in, This represents the new learning rate after scheduling. This represents the lower limit of the learning rate. This represents the current learning rate. factor This represents the attenuation parameter.

[0040] Preferably, the batch normalization BatchNorm1d for:

[0041] ,

[0042] ,

[0043] in, Indicates the first l A normalized value, Indicates the first l One input value, This represents the average value of the current batch. s batch Indicates the variance of the current batch. This represents the final output value of batch normalization. c This represents the scaling parameters that can be learned during training. β This represents the offset parameters that can be learned during training.

[0044] This application provides a machine learning-based prediction system for prestress release loss values. The prediction system applies the above-mentioned prediction method and includes: a data acquisition module, a data partitioning module, a model building module, and a prediction module.

[0045] The data acquisition module uses finite element numerical software to model and simulate the prestressed beam under multiple working conditions, extracts the working parameters and design parameters of the prestressed beam, and performs data preprocessing, distribution checking and feature importance analysis to obtain the initial dataset.

[0046] The data partitioning module is used to divide the initial dataset into an initial training dataset and an initial test dataset and process them to obtain a processed training dataset and a processed test dataset.

[0047] The model building module is used to build a fully connected multilayer perceptron neural network model, define training, validation and monitoring functions, train the fully connected multilayer perceptron neural network model using the processed training dataset, and test the trained model using the processed test dataset to obtain a prediction model.

[0048] The prediction module is used to obtain the actual parameters of the prestressed beam, and based on the actual parameters, the prediction model is used to predict the prestressing release loss value to obtain the prediction result.

[0049] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0050] This invention provides a machine learning-based method for predicting prestressed tension loss values. By combining finite element simulation and deep learning techniques, it achieves high-precision prediction of prestressed engineering tension loss values. Furthermore, this invention provides comprehensive error assessment indicators and intuitive visualization analysis tools to assist in judging prediction reliability, making it easier for users to evaluate the reliability of prediction results and thus providing a scientific basis for engineering decisions. By optimizing tensioning design and controlling the risk of exceeding limits, this invention reduces material waste and construction rework while ensuring structural safety, significantly improving the economy and construction efficiency of the project, and has relatively broad application prospects. Attached Figure Description

[0051] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0053] Figure 2 This is a flowchart of data preprocessing in an embodiment of the present invention;

[0054] Figure 3 This is a schematic diagram of the feature importance ranking results in an embodiment of the present invention;

[0055] Figure 4 This is a schematic diagram of the training process monitoring in an embodiment of the present invention, wherein, Figure 4 (a) in the diagram is a schematic of the training / validation loss. Figure 4(b) in the diagram is a schematic of learning rate scheduling. Figure 4 (c) in the diagram is a schematic diagram of the gradient norm change (first 5). Figure 4 (d) in the diagram represents the final gradient distribution (first 5).

[0056] Figure 5 The determination coefficient R in the embodiments of the present invention 2 Fraction diagram;

[0057] Figure 6 This is a schematic diagram of the model prediction result error in an embodiment of the present invention. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] Example 1:

[0061] In this embodiment, as Figure 1 As shown, a method for predicting prestress release loss based on machine learning includes the following steps:

[0062] S1. Finite element numerical software is used to model and simulate prestressed beams under multiple working conditions, extract the working parameters and design parameters of prestressed beams, and perform data preprocessing, distribution checking and feature importance analysis to obtain the initial dataset.

[0063] The method for obtaining the initial dataset includes: establishing a finite element model and iterating through the dimensions and prestressed tendon height parameters of the prestressed beam; extracting the cross-sectional area, centroid, moment of inertia, and deflection characteristics of the prestressed beam under different working conditions, and eliminating dimensional differences in the extracted parameters to obtain preprocessed data; performing data distribution checks and calculating the linear correlation of features on the preprocessed data, and then using... n _ repeat The perturbation method is used to perform feature importance analysis in MLP to obtain the initial dataset.

[0064] In this embodiment, considering the large amount of diverse data required for universality and generalization, a finite element model was established using the finite element numerical software ANSYS MECHANICAL ENTERPRISE 19.0 to simulate the prestressing tensioning and release process. For generalization modeling, the beam dimensional parameters, namely beam length... L and H Perform a traversal to determine the fixed position height of the prestressing tendons at the support section. The process involves iterating through the prestress loss values ​​after release according to the percentage of control stress. For formulas involving prestress friction loss, the coefficients are adjusted. m With coefficient k Perform a traversal. Considering on-site measurements and design references, select to extract the mid-span cross-sectional area. Centroid of the mid-span section Moment of inertia at mid-span section The beam mid-span deflection under various working conditions after simulation calculation Δy .since Pandas The library introduces based on Numpy of DataFrame After creating a tabular data structure, corresponding regular expressions are written according to the data format of each result file. The paths to each result file are specified, and features are extracted row by row into a DataFrame for temporary storage. Corresponding data index labels are then created, and warnings for empty files / non-matching data are added, along with checks on the number of processed samples and data distribution. After extraction, feature engineering arrays and prediction label arrays are created according to the data index labels described above. Shape checks, variable statistical descriptions, and linear correlation analysis between features and labels, as well as feature MLP importance analysis, are added. The top 50% of features with the highest linear correlation are mid-span deflection. Δy Centroid of the mid-span section Moment of inertia at mid-span section Prestressing tendon height The specific data preprocessing flowchart is as follows: Figure 2 As shown; the specific feature importance ranking results heatmap is as follows. Figure 3 As shown.

[0065] Before performing feature importance analysis in MLP, the original features themselves have different units and dimensions, with significant differences in numerical range. If training is performed directly on them using importance analysis at different scales, the model may incorrectly assign higher weights to certain features simply due to differences in numerical magnitude. Furthermore, large-scale differences in data will lead to significant differences in gradient update magnitudes between different features, causing the optimizer to adjust its strategy in multiple directions, ultimately resulting in difficulty in model convergence and predictions that are purely numerical and detached from reality. To enable data-driven model learning that is independent of data collection units and only reflects the physical influence of parameters, and to eliminate the interference of dimensional differences on the model itself and evaluation metrics to ensure that importance scores objectively reflect the actual physical influence of features, the aforementioned feature array is modified... Z - Score Standardization. Adoption. n _ repeat The perturbation method establishes an MLP regression model consistent with subsequent training, specifying the activation function basis as... relu Classes, optimizers Adam Class, initial learning rate 0.001, maximum iterations 200 n _ repeat With a repeatability of 10 and a random seed of 42, the characteristic of the number of repeatability counts after randomization is calculated—the mean of model importance—and a heatmap is plotted for visualization.

[0066] The standardized functions involved are as follows:

[0067] ,

[0068] in, Z This represents the standardized value. x 0 represents the original feature value. Represents the characteristic mean. s It represents the characteristic standard deviation.

[0069] The activation function is as follows:

[0070] ,

[0071] in, x This represents the input value of the function.

[0072] The optimizer is as follows:

[0073] gradient: ;

[0074] First-order moment estimation: ;

[0075] Second-order moment estimation: ;

[0076] Deviation correction: , ;

[0077] Update parameters: ;

[0078] in, i t Indicates the first t Step parameters, Represents the loss function. Indicates the first t First moment estimate (mean) of the step. This represents the first decay rate threshold (usually 0.9). Indicates the first t Second-order moment estimate of the step (uncentered variance). This represents the second decay rate threshold (usually 0.999). This indicates the element-wise squaring. This represents the first moment of the gradient after bias correction. This represents the second moment of the gradient after bias correction. or Indicates the learning rate. ϵ This represents the batch-standardized numerical stability term (the minimum value constant is used to prevent numerical stability by division by zero).

[0079] The importance calculation formula is as follows:

[0080] ,

[0081] in, Indicates the first j Features X j The importance of model prediction results This represents the model's performance on the original data (e.g., R). 2 (scores or MSE index, etc.) Indicates the use of the first j Features X j The perturbation dataset generated after scrambling the values ​​(i.e., disrupting their relationship with the target). The calculated performance values ​​after the disturbance.

[0082] For example, suppose there is an existing benchmark forecast , for features x 1 or x 2. Proceed n _ repeat Subsequent random perturbations, such as random sampling substitution or adding different types of noise, are used to obtain the perturbation input while keeping other characteristics unchanged. ; Calculate new predicted values ​​for the perturbed samples y iThe degree of change in the predicted value is then obtained, which corresponds to the importance of the perturbation feature. The importance of other features is calculated similarly, that is, by calculating the degree of change in the prediction after randomly perturbing a feature multiple times, the importance of the feature to the prediction is measured.

[0083] S2. Divide the initial dataset into an initial training dataset and an initial test dataset and process them to obtain a processed training dataset and a processed test dataset.

[0084] Methods for obtaining processed training and test datasets include: utilizing train _ test _ split The function proportionally partitions the initial dataset to obtain an initial training set and an initial test set; it then standardizes the initial training set and the initial test set to obtain standardized initial training set and standardized initial test set; finally, it performs tensor transformation on the standardized initial training set and the standardized initial test set and introduces... TensorDataset and DataLoader The transformed training dataset is shuffled to obtain the processed training dataset and the processed test dataset.

[0085] In this embodiment, (1) data partitioning: to facilitate the subsequent use of a dataset independent of the training process to avoid overfitting verification, assist in hyperparameter tuning, and avoid data leakage, etc., self sklearn In the library model _ selection Introduced in China train _ test _ split Dataset partitioning function, defining the proportion of the test set. test _ size=0.2, random seed 42, proportionally divide the original dataset. (2) Data standardization: Use Z-Score standardization in step S1 to avoid possible slow convergence, gradient vanishing or gradient explosion, model over-dependence, training overfitting and training over-oscillation. Based on the above, standardize the features and labels respectively (the training set fits the scaler, and the test set only applies the same scaling parameter), and output them together with the standardizer object for subsequent repetitive calls. (3) PyTorch tensor transformation: In order to fit the MLP neural network architecture built later and unify the computation framework, optimize the batch computation, storage and training performance of the model itself, integrate the built-in functions of torch and the basic configuration of the network layer, apply mathematical support such as differential compatibility and automatic gradient calculation, obtain the standardized data in the previous text and convert it into PyTorch tensors, and flatten the label data according to the output requirements of the regression task. (4) Data loader: In order to accelerate batch loading, out-of-order and multi-process to improve training efficiency, code conciseness and compatibility and functional extensibility within possible complex requirements, the data loader is automatically loaded. torch Inside the library utils Below data Library import TensorDataset and DataLoader Two functions are used: the former combines the tensor arrays processed above and makes them correspond correctly, and the latter sets the batch size, supports random shuffling of the training set, and keeps the test set in order, so as to ensure that the factors affecting the model learning results are simple data features, physical meaning and distribution patterns, etc., and disregard the numerical meaning of the data itself.

[0086] S3. Construct a fully connected multilayer perceptron neural network model, define training, validation, and monitoring functions, train the fully connected multilayer perceptron neural network model using the processed training dataset, and test the trained model using the processed test dataset to obtain the prediction model.

[0087] Methods for obtaining the predictive model include: constructing a fully connected multilayer perceptron neural network model, including: a feature input layer, hidden layers, and an output layer; defining the combination of... LeakyReLU Functions and SiLU The function employs a dual-coupled composite activation function and a forward propagation function; a mean squared error loss function is introduced. MSELoss Optimizer AdamW and dynamic adjustment of learning rate scheduling strategy ReduceLROnPlateau Batch normalization is incorporated into the hidden layer. BatchNorm1d The fully connected multilayer perceptron neural network model is optimized using a hierarchical non-uniform neuron inactivation technique. The optimized fully connected multilayer perceptron neural network model is trained using a processed training dataset, and the trained model is tested using a processed test dataset to obtain a prediction model.

[0088] In this embodiment, an MLP model architecture is established. This is achieved using, but is not limited to, fully connected layer structures and batch normalization. BatchNorm1d Combination SiLU and LeakyReLU The dual activation function and the neuron inactivation layer that decreases layer by layer with increasing dimension. Dropout This involves implementing a nonlinear mapping from feature input to predicted output, thereby providing continuous predicted values ​​for this regression task. The deactivation function is used in low-dimensional, large-parameter layers. LeakyReLU To ensure the avoidance of neuron death and the mitigation of gradient vanishing in the negative region, while providing simple and efficient nonlinearity to reduce computational cost and improve convergence speed, this method is used near the high-dimensional attention mechanism and in the output prediction layer. SiLU This smooth, non-monotonic activation function, leveraging its self-gating properties and more stable gradients, learns more complex patterns or rules, similar to the former. LeakyReLU After alternation and combination, LeakyReLU Initial hard activation and SiLU The high-dimensional soft activation balances model computational cost and learning performance. Batch normalization is introduced between layers. BatchNorm1d and multi-layer deactivation Dropout To enhance training stability while avoiding overfitting / underfitting. Considering the regression task and learning efficiency, a combination of methods is used. AdamW Optimizer MSELoss Mean squared error loss function and specific loss metric monitoring learning rate scheduling strategy ReduceLROnPlateau The layers involved Linear The linear transformation is as follows:

[0089] ,

[0090] in, y Indicates the output vector. v Represents the input vector. Represents the weight matrix. b This represents the bias vector.

[0091] Batch normalization BatchNorm1d for:

[0092] ,

[0093] ,

[0094] in, Indicates the first l A normalized value, Indicates the first l One input value, This represents the average value of the current batch. s batch Indicates the variance of the current batch. This represents the final output value of batch normalization. c This represents the scaling parameters that can be learned during training. β This represents the offset parameters that can be learned during training.

[0095] LeakyReLU The function is:

[0096] ,

[0097] in, max This means taking the maximum of the two values. x This represents the input value of the function. α This represents the negative slope coefficient (usually taken as 0.01).

[0098] SiLU The function is:

[0099] ,

[0100] in, s express Sigmoid function.

[0101] Dropout The following applies only during training; it does not apply to validation and testing:

[0102] ,

[0103] in, m For Bernoulli mask (0 or 1); p This represents the probability of discarding, i.e. Dropout ( p The value varies from 0.1 to 0.5 depending on the specific requirements.

[0104] Mean squared error loss function MSELoss for:

[0105] ,

[0106] in, n This represents the total number of samples. i Indicates the first i One sample, Represents the actual value. This represents the model's predicted value.

[0107] Optimizer AdamW for:

[0108] ,

[0109] in, l This represents the weight decay coefficient;

[0110] Dynamically adjust learning rate scheduling strategy ReduceLROnPlateau for:

[0111] ,

[0112] in, This represents the new learning rate after scheduling. This represents the lower limit of the learning rate. This represents the current learning rate. factor This represents the attenuation parameter.

[0113] above, AdamW The optimizer uses L2 regularization, which is independent of gradient updates and is tuned by a single parameter, thus avoiding the limitations of traditional optimization methods. Adam The coupling problem between weight decay and adaptive learning rate in the optimizer; a unique approach is used for regression problems. MSELoss The mean squared error loss function penalizes large errors more strongly, making the model pay more attention to significant biases, while its continuous differentiability facilitates gradient calculation at a point and makes it consistent with the mean squared error. AdamW The optimization process has better compatibility; ReduceLROnPlateau The learning rate scheduling strategy automatically reduces the learning rate when validation loss stagnates, rather than manually adjusting hyperparameters. This phased reduction of the learning rate helps the model fine-tune hyperparameters and converge towards a better solution when it gets stuck in a potentially local optimum. Combining these strategies can reduce training costs, improve model generalization ability, efficiently optimize the model's learning structure, and enhance robustness. Furthermore, the output results are processed after the model outputs. flatten The flattening operation is designed to suit the needs of gradient calculation and autonomous differentiation during the training process.

[0114] Utilizing the constructed MLP architecture, forward propagation, loss function, optimizer, and learning rate scheduling strategy, a training loop function is defined to implement batch gradient descent; a validation loop function is defined to evaluate the model's performance on the test set and disable gradient computation to save resources; a training monitoring function is defined to record metrics such as training loss, validation loss, learning rate changes, gradient norm, and distribution during training; and an inverse normalization function is defined to restore the prediction results to their original dimensions during subsequent predictions. These self-built functions are then combined to perform a loss-based... loss The training process involves saving the optimal training model and data normalizer. After the training process is complete, the monitoring and visualization section is used to visualize the results in charts and save them. A specific diagram illustrating the monitoring of training process metrics is shown below. Figure 4 As shown.

[0115] For the training loop function, the network mode is specified as the training mode. Before training, the training loss value and the historical monitoring label value are initialized to 0. The gradients of the optimizer model parameters are cleared to prevent gradient accumulation during backpropagation and to ensure the direction of parameter propagation. The training process is repeated in a loop: forward propagation, training loss calculation, loss backpropagation, dynamic gradient clipping, optimizer parameter update, monitoring label recording, and loss accumulation calculation. The relevant formulas for backpropagation and dynamic gradient clipping, which were not mentioned in the previous text, are given below:

[0116] Backpropagation is as follows:

[0117] Chain rule: ;

[0118] Output layer ( MSE ): ;

[0119] in, i Indicates model parameters, N Indicates the batch size of the data. Indicates the predicted output. This represents the actual value of the corresponding predicted output.

[0120] Dynamic gradient clipping is as follows:

[0121] ,

[0122] ,

[0123] in, Indicates the current gradient. This represents the manually set dynamic clipping hyperparameter threshold, which is assigned in this embodiment. minutes (3.0, 1.0+0.05t), t Indicates training rounds, The L2 norm of the gradient is represented. This represents the gradient after clipping.

[0124] The complete training process, as described above, is: initialization (zeroing) — iterative training for each batch — gradient zeroing — forward propagation — back propagation — dynamic gradient clipping — parameter update — convergence or early stopping. For the early stopping mechanism, an improvement patience counter of 10 is given. If the model's validation loss does not improve within 10 iterations (the counter increments by 1 for each iteration the current loss exceeds the optimal loss, up to the upper limit), the optimal validation loss is fixed as the model performance evaluation, and the loop is exited. Training progress is printed every 20 iterations to stabilize the update log output, and additional prompts are given when the learning rate changes.

[0125] For the validation function, specify the network mode as validation mode, initialize the validation loss, disable model gradient calculation and parameter update, call the loss function mentioned above to calculate the validation loss value and return the average validation loss.

[0126] For the training loop, given a total of 200 training epochs, initialize the optimal loss, early stopping counter, training loss, validation loss, learning rate, monitoring function, and monitoring metrics. Iterate through all training epochs, sequentially calling the training and validation function modules and providing hyperparameters to calculate the training and validation losses for the current epoch. Update the monitoring metrics records and adjust the learning rate based on the validation loss. After returning the validation loss (i.e., after the learning rate is dynamically adjusted using the validation loss), return the current learning rate and perform monitoring comparisons to determine whether to update and print a warning. Enable early stopping for the validation loss and simultaneously update the patience counter. After the early stopping check passes or training ends, call `visualize` to visualize the changes in the monitoring metrics during the training process.

[0127] For inverse standardization functions, users or downstream systems need results at the original scale for more intuitive judgment, and evaluation metrics such as MAE are only meaningful when calculated at the original scale. Inverse standardization and inverse transformation are performed on the standardized model output prediction results to restore the predicted values ​​to the scale of the original data. The inverse standardization is as follows:

[0128] ,

[0129] in, This represents the original value after inverse standardization. This represents the standardized value. The standard deviation of the original data is represented by the standard deviation of the original data. This represents the mean of the original data.

[0130] In summary, this project completes the training of an MLP deep learning model, including data standardization, model training, validation, monitoring, and an early stopping mechanism. It ensures training stability and efficiency optimization while providing monitoring tools to help debug model performance and assist in model optimization. The path-based storage of reusable models and normalizers facilitates deployment and inference, ensuring consistency between production and testing environments.

[0131] Load the test dataset from step S2 and perform predictions using the trained model. After standardizing the data using a normalizer consistent with the training process, perform predictions and return the results. Transform the prediction results to their original dimensional scale through inverse standardization and then calculate multiple evaluation metrics, including the coefficient of determination R. 2Three metrics—the score, the mean absolute error (MAE) index, and the root mean square error (RMSE) index—are used to quantitatively evaluate prediction performance (prediction bias). To visually demonstrate the prediction effect, an ideal line fitting the true and predicted values ​​is overlaid to quickly determine the model's systematic bias and generate a histogram of the prediction error distribution. Based on the above-defined prediction function, an interactive deployment is implemented that prompts the user to input different features in sequence and calls the encapsulated prediction function to return the predicted value. A scatter plot of the ideal fit between the true and predicted values ​​is shown below. Figure 5 As shown. The specific prediction error distribution histogram is as follows. Figure 6 As shown. The coefficient of determination R involved. 2 The scores are as follows:

[0132] ,

[0133] The Mean Absolute Error (MAE) exponent is as follows:

[0134] ,

[0135] The root mean square error (RMSE) exponent is as follows:

[0136] ,

[0137] in, This represents the mean of the true values.

[0138] The above describes the process of importing necessary dependencies, loading the original dataset, and calling a normalizer for standardization. With gradients disabled, predictions are made on the test set, and both the predicted and true values ​​are inversely standardized. The returned results are then visualized using different prediction evaluation metrics to show the distribution. Finally, an interactive deployment is added, and the entire process is packaged and encapsulated into a prediction function to provide a convenient and reusable interface for users to input parameters, simplifying the prediction process.

[0139] S4. Obtain the actual parameters of the prestressed beam, and based on the actual parameters, use the prediction model to predict the prestressing release loss value to obtain the prediction result.

[0140] In this embodiment, the machine learning framework dependency library, numerical computation library, file loading library, and related predefined modules are imported, and these are defined as resource loading functions with evaluation mode enabled. After calling the loading function within the integration module, the output and interactive deployment are integrated, encapsulating an end-to-end prediction process system. Compared to repetitive training, the dependency files `model weights.pth` and `normalizer.pkl` after a single training iteration ensure reproducible, automated, and rapid prediction. The preprocessing parts corresponding to model loading and data processing are hidden, ensuring portability and robustness while achieving lightweight deployment, reducing learning memory usage and computational costs. This reduces the technical requirements and ease of use for prediction, making it more user-friendly. Then, the actual parameters of the prestressed beam are obtained, and the prediction model is used to predict the prestressing release loss value, yielding the prediction result.

[0141] Example 2:

[0142] In this embodiment, a machine learning-based system for predicting prestress release loss includes: a data acquisition module, a data partitioning module, a model building module, and a prediction module.

[0143] The data acquisition module uses finite element method (FEM) software to model and simulate prestressed beams under multiple working conditions, extracting the working and design parameters of the prestressed beams. It then performs data preprocessing, distribution checks, and feature importance analysis to obtain the initial dataset. The data partitioning module divides the initial dataset into an initial training dataset and an initial test dataset, and processes them to obtain processed training and test datasets. The model building module constructs a fully connected multilayer perceptron neural network model, defines training, validation, and monitoring functions, trains the fully connected multilayer perceptron neural network model using the processed training dataset, and tests the trained model using the processed test dataset to obtain the prediction model. The prediction module obtains the actual parameters of the prestressed beams and, based on these parameters, uses the prediction model to predict the prestressing release loss value, obtaining the prediction result.

[0144] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for predicting prestress release loss based on machine learning, characterized in that, Includes the following steps: Finite element numerical software was used to model and simulate the prestressed beam under multiple working conditions. The working parameters and design parameters of the prestressed beam were extracted, and data preprocessing, distribution checking and feature importance analysis were performed to obtain the initial dataset. The initial dataset is divided into an initial training dataset and an initial test dataset and processed to obtain a processed training dataset and a processed test dataset. A fully connected multilayer perceptron neural network model is constructed, training, validation, and monitoring functions are defined, the fully connected multilayer perceptron neural network model is trained using the processed training dataset, and the trained model is tested using the processed test dataset to obtain a prediction model. Obtain the actual parameters of the prestressed beam, and based on the actual parameters, use the prediction model to predict the prestress release loss value to obtain the prediction result; The methods for obtaining the initial dataset include: Establish a finite element model and iterate through the dimensions and prestressing tendon height parameters of the prestressed beam; The cross-sectional area, centroid, moment of inertia, and deflection characteristics of the prestressed beam under different working conditions are extracted, and the dimensional differences of the extracted parameters are eliminated to obtain preprocessed data. The preprocessed data is subjected to data distribution checks, feature linear correlation calculations, and then... n _ repeat The initial dataset is obtained by performing feature importance analysis of MLP using the perturbation method.

2. The method for predicting prestress release loss based on machine learning according to claim 1, characterized in that, Methods for obtaining processed training and test datasets include: use train _ test _ split The function divides the initial dataset proportionally to obtain the initial training dataset and the initial test dataset; The initial training dataset and the initial test dataset are standardized to obtain standardized initial training dataset and standardized initial test dataset. The standardized initial training dataset and the standardized initial test dataset are subjected to tensor transformation, and then introduced... TensorDataset and DataLoader The transformed training dataset is shuffled to obtain the processed training dataset and the processed test dataset.

3. The method for predicting prestress release loss based on machine learning according to claim 1, characterized in that, The methods for obtaining the prediction model include: Construct a fully connected multilayer perceptron neural network model, including: a feature input layer, a hidden layer, and an output layer; Definition Combination LeakyReLU Functions and SiLU The doubly coupled composite activation function and the forward propagation function; Introducing the mean squared error loss function MSELoss Optimizer AdamW and dynamic adjustment of learning rate scheduling strategy ReduceLROnPlateau ; The hidden layer incorporates batch normalization. BatchNorm1d The fully connected multilayer perceptron neural network model is optimized using a hierarchical non-uniform neuron inactivation technique. The optimized fully connected multilayer perceptron neural network model is trained using the processed training dataset, and the trained model is tested using the processed test dataset to obtain the prediction model.

4. The method for predicting prestress release loss based on machine learning according to claim 3, characterized in that, The LeakyReLU The function is: ， in, max This means taking the maximum of the two values. x This represents the input value of the function. α Indicates the negative slope coefficient; The SiLU The function is: ， in, σ express Sigmoid function.

5. The method for predicting prestress release loss based on machine learning according to claim 3, characterized in that, The mean square error loss function MSELoss for: ， in, n This represents the total number of samples. i Indicates the first i One sample, Represents the actual value. Indicates the model's predicted value; The optimizer AdamW for: ， in, η Indicates the learning rate. This represents the first moment of the gradient after bias correction. This represents the second moment of the gradient after bias correction. λ This represents the weight decay coefficient. Represents the batch-standardized numerically stable term. θ t Indicates the first t Step parameters; The dynamic learning rate adjustment scheduling strategy ReduceLROnPlateau for: ， in, This represents the new learning rate after scheduling. This represents the lower limit of the learning rate. This represents the current learning rate. factor This represents the attenuation parameter.

6. The method for predicting prestress release loss based on machine learning according to claim 5, characterized in that, The batch normalization BatchNorm1d for: ， ， in, Indicates the first l A normalized value, Indicates the first l One input value, This represents the average value of the current batch. σ batch Indicates the variance of the current batch. This represents the final output value of batch normalization. γ This represents the scaling parameters that can be learned during training. β This represents the offset parameters that can be learned during training.

7. A machine learning-based system for predicting prestressed tension loss values, wherein the prediction system applies the prediction method according to any one of claims 1-6, characterized in that, include: Data acquisition module, data partitioning module, model building module, and prediction module; The data acquisition module uses finite element numerical software to model and simulate the prestressed beam under multiple working conditions, extracts the working parameters and design parameters of the prestressed beam, and performs data preprocessing, distribution checking and feature importance analysis to obtain the initial dataset. The data partitioning module is used to divide the initial dataset into an initial training dataset and an initial test dataset and process them to obtain a processed training dataset and a processed test dataset. The model building module is used to build a fully connected multilayer perceptron neural network model, define training, validation and monitoring functions, train the fully connected multilayer perceptron neural network model using the processed training dataset, and test the trained model using the processed test dataset to obtain a prediction model. The prediction module is used to obtain the actual parameters of the prestressed beam, and based on the actual parameters, the prediction model is used to predict the prestress release loss value to obtain the prediction result.

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