Wooden arch bridge parameter intelligent design method based on two-stage prediction model
Through the two-stage prediction model, SSA-XGBoost and CF-BPNN algorithms are used, combined with expert knowledge and feature importance analysis, the problem of parameter dependence experience in traditional wooden arcade bridge design is solved, and the rapid and accurate prediction of the vector span ratio and seedling root diameter is achieved, which improves the scientificity and rationality of the design.
Patent Information
- Application Number
- CN202510395283.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-31
- Publication Date
- 2025-07-01
AI Technical Summary
In the design of traditional wooden arcade bridges, core parameters such as the vector span ratio and seedling root diameter rely on craftsmen's experience, and there are regional limitations and lack of quantitative basis, resulting in significant design differences. The inheritance of experience is on the verge of generations, making it difficult to adapt to the complex geographical environment and modern construction needs.
A two-stage prediction model is adopted, first predicting the vector-span ratio based on the SSA-XGBoost algorithm, and then predicting the seedling root diameter based on the CF-BPNN network model. Combining expert knowledge and feature importance analysis, input parameter selection is optimized, and an intelligent design system is constructed.
It realizes fast and accurate prediction of the vector span ratio and seedling root diameter, improves the scientificity and rationality of the design, reduces the dependence on expert experience, and provides technical support for the scientific inheritance and innovation of traditional skills.
Smart Images
Figure CN120234879A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of the structural design of wooden arch bridges, and particularly relates to an intelligent design method for the parameters of wooden arch bridges based on a two-stage prediction model. Background Art
[0002] The wooden arch bridge is an outstanding representative of traditional Chinese wooden bridges. Its unique "three-section seedlings - five-section seedlings" double-layer arch frame system forms a stable force-bearing network through the interpenetrating and overlapping of short wooden components, reflecting the ancient craftsmen's profound understanding of material mechanics. Among the more than a hundred Ming and Qing wooden arch bridges existing in the Fujian and Zhejiang regions, 90% adopt this structure, becoming an important carrier for studying traditional construction techniques and structural mechanics, and being listed in the UNESCO Intangible Cultural Heritage List in Urgent Need of Protection.
[0003] In traditional construction, core parameters such as the rise-span ratio and the root diameter of the seedlings rely on the inheritance of craftsmen's experience. Although these experiences are effective in historical practices, they have significant limitations: First, regional experiences are difficult to adapt to complex geographical environments (such as high-altitude strong wind areas, humid river valleys); second, the determination of parameters lacks quantitative basis, resulting in significant differences in the designs of bridges with the same span. Although recent research has made progress in structural analysis, it mostly focuses on the statistics of historical cases and static analysis, lacking a design parameter prediction method for modern construction. In addition, the intensifying crisis in the inheritance of construction techniques has increased the demand for technological innovation, and the inheritance of experience is on the verge of being cut off. Summary of the Invention
[0004] The purpose of the present invention is to provide an intelligent design method for the parameters of wooden arch bridges based on a two-stage prediction model, which can quickly and accurately predict the rise-span ratio and the root diameter of the seedlings of wooden arch bridges.
[0005] To achieve the above purpose, the technical solution adopted by the present invention is: an intelligent design method for the parameters of wooden arch bridges based on a two-stage prediction model, including the following steps:
[0006] S1: Data acquisition and processing: Acquire the design data of historical wooden arch bridges and extract the key design parameters and target output parameters from them, and then preprocess the extracted data; the key design parameters include the length, width, span, and number of arch ribs of the wooden arch bridge, and the target output parameter is the diameter range of each seedling;
[0007] S2: First-stage model prediction: Based on the SSA-XGBoost algorithm, construct a first-stage prediction model, input the length, width, span, and number of arch ribs of the wooden arch bridge, and output the predicted value of the rise-span ratio;
[0008] S3: Second-stage model prediction: Based on the cascaded forward BP neural network (CF-BPNN) integrating expert knowledge, construct a second-stage prediction model. Input the predicted values of the length, width, span, number of arch ribs, and rise-span ratio of the wooden arch bridge, and output the predicted values of the root diameter range of each section of the seedlings.
[0009] S4: Model evaluation and verification: Use the performance evaluation indicators of machine learning models to quantify the model performance, and determine the contribution degree of each input parameter to the prediction result based on the feature importance analysis to optimize the selection of input parameters.
[0010] Furthermore, in step S1, obtain the historical design data of wooden arch bridges through historical design documents and measured data, and then extract the key design parameters and target output parameters of wooden arch bridges from the obtained historical design data of wooden arch bridges.
[0011] Data preprocessing includes:
[0012] Use the Min-Max normalization method to normalize numerical data, map the data to the [0,1] interval to improve the stability of model training.
[0013] Eliminate outliers through the box plot method to avoid the influence of outliers on model training.
[0014] Use the K-nearest neighbor interpolation (KNN) method to fill in missing values to improve data integrity.
[0015] Furthermore, the SSA-XGBoost algorithm uses the sparrow search algorithm (SSA) to optimize the hyperparameters of the XGBoost model, improving the accuracy and generalization ability of the rise-span ratio prediction; in the network training process of the CF-BPNN network model, expert knowledge constraints are introduced to make the predicted root diameter of the seedlings conform to the mechanical properties and design specifications of wooden arch bridges.
[0016] Furthermore, in step S2, based on the SSA-XGBoost algorithm, construct a first-stage prediction model, and its implementation method is:
[0017] Construct an XGBoost regression model, with the length, width, span, and number of arch ribs of the wooden arch bridge as inputs and the rise-span ratio as the output.
[0018] Use the sparrow search algorithm (SSA) to optimize the hyperparameters of the XGBoost regression model, including the learning rate, maximum depth, and subsampling rate, to improve the prediction accuracy and generalization ability of the model.
[0019] Evaluate the model performance based on K-fold cross-validation and select the optimal parameter configuration.
[0020] Furthermore, in step S3, a second-stage prediction model is constructed based on the cascaded forward BP neural network (CF-BPNN) integrating expert knowledge, and its implementation method is as follows:
[0021] Adopt a cascaded forward network architecture to enable each cascaded module to fully learn feature information at different levels;
[0022] Introduce expert knowledge constraints into the loss function, including the relationship between the total diameter of three-section seedlings and five-section seedlings and the bridge width;
[0023] Optimize the model training process through an adaptive learning rate adjustment strategy to ensure that the model can converge efficiently at different training stages.
[0024] Furthermore, the input of the second-stage prediction model is the design parameter values that vary due to the conditions and environment of the wooden arch bridge, including: the length, width, span, number of arch ribs, and rise-span ratio of the wooden arch bridge. The output of the second-stage prediction model is the range values of the root diameters of each section of seedlings, including: the flat seedling root diameter of three-section seedlings, the inclined seedling root diameter of three-section seedlings, the flat seedling root diameter of five-section seedlings, the upper inclined seedling root diameter of five-section seedlings, and the lower inclined seedling root diameter of five-section seedlings.
[0025] Furthermore, the second-stage prediction model optimizes the model parameters through the backpropagation algorithm and introduces constraint conditions related to expert knowledge into the loss function; the total loss L introduced with expert knowledge constraints is:
[0026]
[0027] Among them, Loss is the loss function, y, respectively represent the true value and the predicted value, N is the total number of samples, λ is the penalty coefficient, Penalty(x) is the constraint condition function related to expert knowledge, and this constraint condition is: the sum of the diameter of three-section seedlings multiplied by the number of roots plus the diameter of five-section seedlings multiplied by the number of roots should be less than the bridge width and there should be a certain redundancy value. Its expression is:
[0028] D3×n3 + D5×n5 < d + δ
[0029] Among them, D3 is the diameter of three-section seedlings, n3 is the number of three-section seedlings, D5 is the diameter of five-section seedlings, n5 is the number of five-section seedlings, d is the width of the whole bridge, and δ is the set redundancy value; construct the constraint condition function based on this constraint condition as follows:
[0030] Penalty(x) = max(0, D3×n3 + D5×n5 - d - δ)
[0031] By adding the penalty term λ·Penalty(x) to the loss function, when the constraint condition is violated, the penalty value increases, thereby guiding the model to generate solutions that meet the engineering constraints during the optimization process.
[0032] Further, in step S4, the performance evaluation indexes of the first-stage prediction model are Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Coefficient of Determination (R 2 ), and the performance evaluation indexes of the second-stage prediction model are Mean Square Error (MSE), Mean Absolute Percentage Error (MAPE), and Residual Sum of Squares (RSS).
[0033] Further, in step S4, the feature importance analysis adopts Shapley value (SHAP), the method of decreasing mean square error, or gain coefficient to quantify the contribution degree of input parameters to the prediction result, so as to ensure that the model focuses on the key parameters with higher contribution degrees to the prediction of the rise-span ratio and the root diameter of the joint seedlings, thereby improving the interpretability of the model.
[0034] The present invention also provides an intelligent parameter design system for wooden arch bridges based on a two-stage prediction model, including a memory, a processor, and computer program instructions stored on the memory and capable of being run by the processor. When the processor runs the computer program instructions, the above method can be implemented.
[0035] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides an intelligent parameter design method for wooden arch bridges based on a two-stage prediction model. This method can scientifically predict the rise-span ratio and the root diameter of the joint seedlings quickly and accurately, obtain design parameters that meet the engineering reality, and improve the scientificity and rationality of the bridge structure design; this method can provide reliable technical support for the parametric design and structural safety assessment of wooden arch bridges, reduce the design dependence on expert experience, effectively make up for the deficiencies of traditional empirical rules, and lay a foundation for the scientific inheritance and innovative application of intangible cultural heritage techniques. BRIEF DESCRIPTION OF THE DRAWINGS
[0036] Figure 1 is a flowchart of the implementation of the intelligent parameter design method for wooden arch bridges based on a two-stage prediction model provided by an embodiment of the present invention;
[0037] Figure 2 is a flowchart of the implementation of the first-stage prediction model constructed based on the SSA-XGBoost algorithm in an embodiment of the present invention;
[0038] Figure 3 is a graph of the feature importance analysis result in an embodiment of the present invention;
[0039] Figure 4 is a comparison graph of the predicted value and the actual value in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0040] The present invention will be further described below with reference to the drawings and embodiments.
[0041] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.
[0042] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0043] As Figure 1 shown, this embodiment provides an intelligent design method for the parameters of a wooden arch bridge based on a two-stage prediction model, including the following steps:
[0044] S1: Data acquisition and processing: Obtain historical wooden arch bridge design data and extract key design parameters and target output parameters therefrom, and then preprocess the extracted data; the key design parameters include the length, width, span, and number of arch ribs of the wooden arch bridge, and the target output parameter is the diameter range of each section of the seedlings.
[0045] S2: First-stage model prediction: Build a first-stage prediction model based on the SSA-XGBoost algorithm, input the length, width, span, and number of arch ribs of the wooden arch bridge, and output the predicted value of the rise-to-span ratio.
[0046] S3: Second-stage model prediction: Build a second-stage prediction model based on the cascaded forward BP neural network (CF-BPNN) that integrates expert knowledge, input the length, width, span, number of arch ribs, and predicted value of the rise-to-span ratio of the wooden arch bridge, and output the predicted value of the root diameter range of each section of the seedlings.
[0047] S4: Model evaluation and verification: Quantify the model performance using machine learning model performance evaluation metrics, and determine the contribution degree of each input parameter to the prediction result based on feature importance analysis to optimize the selection of input parameters.
[0048] 1. Data acquisition and processing
[0049] Historical wooden arch bridge design data can be obtained through historical design documents and measured data, and then the key design parameters and target output parameters of the wooden arch bridge can be extracted from the obtained historical wooden arch bridge design data.
[0050] In this embodiment, field measured data of more than 130 wooden arch bridges in Fujian and Zhejiang are obtained, and then key design parameters and target output parameters are extracted therefrom, including but not limited to the length, width, span, number of arch ribs and root diameter range of each section of the wooden arch bridges.
[0051] In order to ensure data quality, the following preprocessing methods are used to preprocess the extracted data:
[0052] 1) The Min-Max normalization method is used to normalize the numerical data and map the data to the [0,1] interval to improve the stability of model training;
[0053] 2) Remove outliers through the box plot method to avoid outliers affecting model training;
[0054] 3) K nearest neighbor interpolation (KNN) method is used to fill missing values to improve data completeness.
[0055] 2. First-stage model prediction
[0056] The SSA-XGBoost algorithm uses the sparrow search algorithm (SSA) to optimize the hyperparameters of the XGBoost model to improve the accuracy and generalization ability of the arrow-to-span ratio prediction.
[0057] The first-stage prediction model is constructed based on the SSA-XGBoost algorithm, and its implementation method is as follows:
[0058] a. Construct an XGBoost regression model with the length, width, span and number of arch ribs of the wooden arch bridge as input and the span-rise ratio as output;
[0059] b. Use the sparrow search algorithm (SSA) to optimize the hyperparameters of the XGBoost regression model, including learning rate, maximum depth, and subsampling rate, to improve the prediction accuracy and generalization ability of the model;
[0060] c. Evaluate model performance based on K-fold cross validation (K=5) and select the optimal parameter configuration;
[0061] d. Input the length, width, span and number of arch ribs of the wooden arch bridge, and output the first-stage prediction result, i.e., the rise-to-span ratio of the wooden arch bridge.
[0062] 3. Second stage model prediction
[0063] The CF-BPNN network model introduces expert knowledge constraints during the network training process, so that the predicted root diameter of the seedlings conforms to the mechanical characteristics and design specifications of the wooden arch bridge.
[0064] The second-stage prediction model is constructed based on the cascade forward BP neural network (CF-BPNN) integrating expert knowledge. The implementation method is as follows:
[0065] a. Adopt a cascaded forward network architecture to enable each cascaded module to fully learn feature information at different levels;
[0066] b. Introduce expert knowledge constraints into the loss function, including the relationship between the sum of the diameters of three - section seedlings and five - section seedlings and the width of the bridge;
[0067] c. Optimize the model training process through an adaptive learning rate adjustment strategy, dynamically adjust the learning rate during training to ensure that the model can converge efficiently at different training stages, thereby improving the model convergence speed and preventing it from falling into local optimal solutions.
[0068] d. Input the rise - span ratio predicted in the first stage and the length, width, span, and number of arch ribs of the wooden arch bridge, and output the root diameter range of each section of the seedlings.
[0069] The second - stage prediction model takes the design parameter values that vary due to the conditions and environment of the wooden arch bridge, such as the length, width, span, number of arch ribs, and rise - span ratio of the wooden arch bridge, as inputs, and takes the range values (maximum and minimum values) of the root diameters of each section of the seedlings (the flat - root diameter of the three - section seedling, the inclined - root diameter of the three - section seedling, the flat - root diameter of the five - section seedling, the upper - inclined - root diameter of the five - section seedling, and the lower - inclined - root diameter of the five - section seedling) as outputs.
[0070] During the training process of the second - stage prediction model, optimize the model parameters through the backpropagation algorithm and introduce constraint conditions related to expert knowledge into the loss function.
[0071] The total loss L with expert knowledge constraints is:
[0072]
[0073] where Loss is the loss function, y, represent the true value and the predicted value respectively, N is the total number of samples, λ is the penalty coefficient, Penalty(x) is the constraint - condition function related to expert knowledge, and the constraint condition is: the sum of the diameter of the three - section seedlings multiplied by the number of roots plus the diameter of the five - section seedlings multiplied by the number of roots should be less than the width of the bridge and there should be a certain redundancy value. Its expression is:
[0074] D3×n3 + D5×n5 < d + δ
[0075] where D3 is the diameter of the three - section seedlings, n3 is the number of three - section seedlings, D5 is the diameter of the five - section seedlings, n5 is the number of five - section seedlings, d is the width of the entire bridge, and δ is the set redundancy value.
[0076] Construct the constraint - condition function based on this constraint condition as follows:
[0077] Penalty(x) = max(0, D3×n3 + D5×n5 - d - δ)
[0078] By adding the penalty term λ·Penalty(x) to the loss function, the penalty value increases when the constraint is violated, thereby guiding the model to generate a solution that meets the engineering constraints during the optimization process.
[0079] 4. Model evaluation and validation
[0080] The mean absolute error (MAE), root mean square error (RMSE) and coefficient of determination (R 2 ) These three evaluation indicators evaluate the performance of the first-stage prediction model, and their specific expressions are:
[0081]
[0082]
[0083] In the formula, m is the total number of samples; y, represent the true value, predicted value and average value respectively.
[0084] The performance of the second-stage prediction model is evaluated using three evaluation indicators: mean square error (MSE), mean absolute percentage error (MAPE) and residual sum of squares (RSS). The calculation formula is as follows:
[0085]
[0086] Where n is the total number of samples; y, represent the true value, predicted value and average value respectively.
[0087] Based on feature importance analysis, including but not limited to Shapley value (SHAP), mean square error reduction method (MSEReduction) or gain coefficient, the contribution of input parameters to the prediction results is quantified to optimize the selection of input parameters, thereby ensuring that the model focuses on key parameters with higher contribution to the prediction of vector span ratio and node root diameter, so as to improve the interpretability of the model.
[0088] The feature importance analysis results in this example are as follows Figure 3 shown.
[0089] In this embodiment, the feasibility of this method is verified by actual engineering applications. The Longjing Bridge and Guangfu Bridge in a certain city are selected as typical cases, and the design parameters of the two covered bridges and the corresponding measured data of the root diameter of the seedlings are collected, and then input into the trained prediction model to output the predicted values of the span ratio and the root diameter of each seedling.
[0090] Figure 4The comparison between the predicted values and the actual values in this embodiment is shown. In this embodiment, the errors between the predicted values and the actual measured values are all controlled within 8.2%, verifying the high precision and stability of this method in predicting the design parameters of wooden arch bridges. It can effectively assist bridge designers in structural optimization, improve the design rationality, reduce the dependence on empirical judgment, and provide a scientific basis and engineering application value for the intelligent and parametric design of wooden arch bridges.
[0091] The present invention provides an intelligent design method for wooden arch bridge parameters based on a two-stage prediction model, which realizes the high-precision prediction of the rise-span ratio and the range of the root diameter of the joint seedlings, reduces the dependence on the experience of craftsmen, and improves the scientificity of the design of wooden arch bridges. Through actual verification, it shows that the prediction error rate of this method on the measured data set is less than 8.2%, which is significantly better than the traditional empirical method and the single machine learning model. It can provide theoretical support and technical means for the parametric design and material selection of wooden arch bridges, and has high engineering application value.
[0092] This embodiment also provides an intelligent design system for wooden arch bridge parameters based on a two-stage prediction model, including a memory, a processor, and computer program instructions stored on the memory and capable of being run by the processor. When the processor runs the computer program instructions, the above method can be realized.
[0093] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0094] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of the processes and / or blocks in the flowchart and / or block diagram can also be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for realizing the specified functions in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.
[0095] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a particular manner, such that the instructions stored in the computer-readable memory produce a manufacture including an instruction device that implements the functions specified in one or more of the processes Figure 1 and / or boxes Figure 1 specified in one or more of the boxes.
[0096] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operational steps are performed on the computer or other programmable device to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more of the processes Figure 1 and / or boxes Figure 1 specified in one or more of the boxes.
[0097] As described above, it is only the preferred embodiment of the present invention, and it is not a limitation to the present invention in other forms. Any person skilled in the art may use the technical content disclosed above to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still fall within the protection scope of the technical solution of the present invention.
Claims
1. A method for intelligent design of wooden arch bridge parameters based on a two-stage prediction model, characterized in that: The following steps are involved: S1: Data acquisition and processing: Acquire the design data of historical wooden arch bridges and extract key design parameters and target output parameters from them, and then pre-process the extracted data; the key design parameters include the length, width, span and number of arch ribs of the wooden arch bridge, and the target output parameter is the diameter range of each node seedling; S2: First-stage model prediction: The first-stage prediction model is constructed based on the SSA-XGBoost algorithm. The length, width, span and number of arch ribs of the wooden arch bridge are input, and the predicted value of the rise-to-span ratio is output; S3: Second stage model prediction: The second stage prediction model is constructed based on the cascade forward BP neural network (CF-BPNN) integrated with expert knowledge. The predicted values of the length, width, span, number of arch ribs and span-rise ratio of the wooden arch bridge are input, and the predicted values of the root diameter range of each section seedling are output; S4: Model evaluation and validation: Use machine learning model performance evaluation indicators to quantify model performance, and determine the contribution of each input parameter to the prediction result based on feature importance analysis to optimize input parameter selection.
2. The method for intelligent design of wooden arch bridge parameters based on a two-stage prediction model according to claim 1 is characterized in that: In step S1, the design data of historical wooden arch bridges are obtained through historical design documents and measured data, and then the key design parameters and target output parameters of the wooden arch bridges are extracted from the obtained design data of historical wooden arch bridges; Data preprocessing includes: The Min-Max normalization method is used to normalize the numerical data and map the data to the [0,1] interval to improve the stability of model training; Outliers are removed through the box plot method to prevent them from affecting model training; The K nearest neighbor (KNN) method was used to fill in missing values to improve data completeness.
3. The method for intelligent design of wooden arch bridge parameters based on a two-stage prediction model according to claim 1 is characterized in that: The SSA-XGBoost algorithm uses the sparrow search algorithm (SSA) to optimize the hyperparameters of the XGBoost model to improve the accuracy and generalization ability of the rise-to-span ratio prediction. The CF-BPNN network model introduces expert knowledge constraints during the network training process, so that the predicted root diameter of the seedlings conforms to the stress characteristics and design specifications of the wooden arch bridge.
4. The method for intelligent design of wooden arch bridge parameters based on a two-stage prediction model according to claim 1 is characterized in that: In step S2, the first-stage prediction model is constructed based on the SSA-XGBoost algorithm, and its implementation method is as follows: An XGBoost regression model was constructed, with the length, width, span and number of arch ribs of the wooden arch bridge as input and the span-rise ratio as output. The sparrow search algorithm (SSA) is used to optimize the hyperparameters of the XGBoost regression model, including learning rate, maximum depth, and subsampling rate, to improve the prediction accuracy and generalization ability of the model; The model performance was evaluated based on K-fold cross validation and the optimal parameter configuration was selected.
5. The method for intelligent design of wooden arch bridge parameters based on a two-stage prediction model according to claim 1 is characterized in that: In step S3, the second-stage prediction model is constructed based on the cascade forward BP neural network (CF-BPNN) integrating expert knowledge, and the implementation method is as follows: A cascaded forward network architecture is used to enable each cascade module to fully learn feature information at different levels; Expert knowledge constraints were introduced into the loss function, including the relationship between the sum of the diameters of three-node seedlings and five-node seedlings and the width of the bridge; The model training process is optimized through an adaptive learning rate adjustment strategy to ensure that the model can converge efficiently at different training stages.
6. The method for intelligent design of wooden arch bridge parameters based on a two-stage prediction model according to claim 5 is characterized in that: The input of the second-stage prediction model is the design parameter values that change due to the conditions and environment of the wooden arch bridge, including: the length, width, span, number of arch ribs and span-rise ratio of the wooden arch bridge; the output of the second-stage prediction model is the range value of the root diameter of each node seedling, including: the flat root diameter of three-node seedlings, the oblique root diameter of three-node seedlings, the flat root diameter of five-node seedlings, the upper oblique root diameter of five-node seedlings and the lower oblique root diameter of five-node seedlings.
7. The method for intelligent design of wooden arch bridge parameters based on a two-stage prediction model according to claim 5 is characterized in that: The second-stage prediction model optimizes the model parameters through the back propagation algorithm and introduces constraints related to expert knowledge into the loss function; the total loss L with the introduction of expert knowledge constraints is: Among them, Loss is the loss function, y, represents the true value and the predicted value respectively, N is the total number of samples, λ is the penalty coefficient, and Penalty(x) is the constraint function related to expert knowledge. The constraint condition is that the sum of the diameter of the three-node seedling multiplied by the number of roots plus the diameter of the five-node seedling multiplied by the number of roots must be less than the width of the bridge, and there must be a certain redundancy value. Its expression is: D3×n3+D5×n5 <d+δ Among them, D3 is the diameter of three-node seedlings, n3 is the number of three-node seedlings, D5 is the diameter of five-node seedlings, n5 is the number of five-node seedlings, d is the width of the whole bridge, and δ is the set redundancy value; based on this constraint condition, the constraint condition function is constructed as follows: Penalty(x)=max(0,D3×n3+D5×n5-d-δ) By adding the penalty term λ·Penalty(x) to the loss function, the penalty value increases when the constraint is violated, thereby guiding the model to generate a solution that meets the engineering constraints during the optimization process.
8. The method for intelligent design of wooden arch bridge parameters based on a two-stage prediction model according to claim 1 is characterized in that: In step S4, the performance evaluation indicators of the first-stage prediction model are mean absolute error (MAE), root mean square error (RMSE) and determination coefficient (R 2 ), the performance evaluation indicators of the second stage prediction model are mean square error (MSE), mean absolute percentage error (MAPE) and residual sum of squares (RSS).
9. The method for intelligent design of wooden arch bridge parameters based on a two-stage prediction model according to claim 1 is characterized in that: In step S4, the feature importance analysis uses Shapley value (SHAP), mean square error decreasing method or gain coefficient to quantify the contribution of input parameters to the prediction results, thereby ensuring that the model focuses on key parameters with higher contribution to the prediction of vector span ratio and node root diameter, so as to improve the interpretability of the model.
10. An intelligent design system for wooden arch bridge parameters based on a two-stage prediction model, characterized in that: The method comprises a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method according to any one of claims 1 to 9 can be implemented.