https://doi.org/10.5061/dryad.5mkkwh7k9

Data Files

• Seismic_Bridge_Design_Dataset.zip – Contains all MATLAB scripts, SAP2000 model files (including open formats), training data, and optimization results.

Description of the Data and File Structure

The dataset is organized into five main folders. All missing data are represented as NaN or handled appropriately in the code.

Folder 1: 1 SAP 2000 FEM model

This folder contains the SAP2000 v10 finite element models of two cable-stayed bridges (M1 and M2) and an Excel file with information about the ground motions used in the nonlinear time history analyses.
To improve accessibility, the model files are provided in three formats:

• SAP2000 proprietary format (.SDB) – can be opened directly with SAP2000 v10.
• SAP2000 text format (.s2k) – a plain text file that contains the full model definition. This file can be viewed and edited with any text editor and can be imported into SAP2000 or other structural analysis software that supports the SAP2000 .s2k format.
• Excel format (.xls) – an export of the model data in a tabular layout, readable by Microsoft Excel and open-source spreadsheet applications (e.g., LibreOffice Calc, Google Sheets). This format allows users to inspect model parameters (geometry, material properties, loads, etc.) without specialized software.

The following files are included:

• M1.SDB, M1.s2k, M1.xls
  SAP2000 model of the reference bridge (M1). It includes:
  • Geometry: main span 1088 m, tower height 297.7 m, deck width, etc.
  • Material properties for concrete and steel.
  • Load cases: dead load, live load, and three earthquake ground motions (El Centro, Kobe, Northridge) with PGA scaled to values between 0.1g and 0.5g.
  • The model is designed to be run in batch mode via the SAP2000 OAPI (Open Application Programming Interface) from MATLAB for parametric studies.
• M2.SDB, M2.s2k, M2.xls
  SAP2000 model of the target bridge (M2), which has a different structural configuration from M1. It is used to generate a small set of high‑fidelity data for transfer learning calibration. The model includes the same types of load cases as M1 but with modified geometry and material properties.
• Motion-information.xls
  Microsoft Excel file containing metadata and parameters of the earthquake ground motions used in the analyses. It does not contain the actual acceleration time histories but rather information such as:
  • Earthquake name (e.g., El Centro, Kobe, Northridge)
  • Recording station
  • Original PGA (g)
  • Duration (s)
  • Other relevant characteristics (e.g., predominant period)
    This file helps users understand the seismic inputs applied to the bridge models. The actual time history files are not included in the dataset; users must obtain them separately or use the information provided to select compatible records.

Folder 2: 2 Neural network model

This folder contains MATLAB scripts and data used to train three types of neural network surrogates (BPNN, GRNN, RBFN) on the dataset generated from the M1 bridge.

• BPNN.m
  MATLAB script that trains a Back-Propagation Neural Network (BPNN) surrogate.
  • Inputs: 7 design variables: PGA (g), damping coefficient C (kN·(s/m)^α), velocity exponent α (-), main span length L (m), tower height H (m), first two natural periods T₁ (s) and T₂ (s).
  • Outputs: 4 seismic responses: maximum deck displacement D_max (m), base moment M_base (kN·m), maximum damper force F_dmax (kN), and damper stroke δ_d (m).
  • The script uses the newff function and trains the network with the Levenberg–Marquardt algorithm (trainlm). The trained network and normalization parameters are saved as trained_model1.mat.
• GRNN.m
  MATLAB script that trains a General Regression Neural Network (GRNN) surrogate using newgrnn. The input/output structure is identical to that of BPNN.
• RBFN.m
  MATLAB script that trains a Radial Basis Function Network (RBFN) surrogate. It can use either newrb (incremental) or newrbe (exact). The best-performing RBFN model is saved as trained_model1.mat.
• trained_model1.mat
  MAT-file containing the trained neural network model (by default, the RBFN model) and the normalization parameters.
  • net: the neural network object.
  • ps_input: a structure with settings for input normalization (mapminmax).
  • ps_output: a structure with settings for output normalization.
• M1-DataSet-in.xlsx
  Excel file containing the input-output dataset used to train the M1 surrogate. The data were generated by running parametric analyses on the M1 SAP2000 model.
  • Columns 1–7: input design variables (PGA, C, α, L, H, T₁, T₂).
  • Columns 8–11: output seismic responses (D_max, M_base, F_dmax, δ_d).
  • Units are as described above. The dataset contains several thousand samples covering the design space.

Folder 3: 3 Transfered surrogate model

This folder contains the MATLAB implementation of the transfer learning procedure that adapts the M1 surrogate to the M2 bridge using a limited number of new FEA results from M2.

• main_transfer_learning_complete.m
  Main script that performs the complete transfer learning calibration.
  Workflow:
  1. Loads the pre-trained M1 RBFN model from trained_model1.mat (assumed to be located in the parent directory or copied here).
  2. Loads the M2 FEA data from M2_FEA_results.mat (this file is not included in the dataset; users must generate it by running the M2 SAP2000 model with the design points from the sampling scripts).
  3. Analyzes the M2 data, detects constant features, and computes normalization parameters.
  4. Evaluates the direct transfer performance (i.e., applying the M1 model directly to M2 data).
  5. Generates augmented data (500 samples) by perturbing the existing M2 points.
  6. Extracts the RBF centers and spread from the pre-trained network and re-trains the output layer using ridge regression with an optimized regularization parameter.
  7. Performs cross-validation to select the best regularization parameter.
  8. Saves the calibrated model as M2_calibrated_model_complete.mat and the performance comparison as M2_performance_results.mat.
  9. Produces diagnostic plots (scatter plots of predictions vs. true values) saved as M2_calibration_results.png.
     Input required: M2_FEA_results.mat (structure with fields X (N×7) and Y (N×4), or a matrix with 11 columns where the first seven are inputs and the last four are outputs).

Folder 4: 4 Hybrid Surrogate optimization Framework

This folder contains the code for multi-objective optimization of FVD parameters (C, α) using the enhanced surrogate model obtained after transfer learning.

• main_FVD_optimization.m
  MATLAB script that performs NSGA-II multi-objective optimization to minimize the two conflicting objectives: D_max and F_dmax, subject to constraints on M_base, δ_d, and F_dmax.
  Workflow:
  1. Loads the enhanced surrogate model from trained_model_enhanced.mat (which should be the output of the transfer learning script).
  2. Sets the bridge parameters (PGA, L, H, T₁, T₂) and constraint limits (allowable moment, allowable stroke, damper force capacity).
  3. Defines the objective functions and constraints using the surrogate model.
  4. Runs gamultiobj with a smart initial population that includes both extreme and intermediate points.
  5. After optimization, analyzes the Pareto front, computes performance metrics, and selects a recommended optimal solution using a normalized distance approach.
  6. Classifies the Pareto solutions into three design types:
     • High-performance design (minimizes D_max – seismic priority)
     • Economical design (minimizes F_dmax – cost priority)
     • Balanced design (compromise between the two)
  7. Saves all results in a new folder optimization_results_enhanced/, including:
     • results_enhanced.mat: complete MATLAB data structure.
     • pareto_solutions_enhanced.xlsx: all Pareto-optimal points with their design variables and performance.
     • classified_designs.xlsx: the three representative design points.
     • Figures: optimization_results_enhanced.png and design_classification.png (also as .fig files).
     • plot_data/ subfolder containing the raw data for the figures in CSV format and a MATLAB script redraw_optimization_plots.m to regenerate the plots from the saved data.
• trained_model_enhanced.mat
  MAT-file containing the enhanced surrogate model (RBFN) after transfer learning. It includes the same fields as trained_model1.mat: net, ps_input, ps_output.

Folder 5: 5 Sampling

This folder contains MATLAB scripts for two sampling strategies used to generate the calibration points for transfer learning.

• sample_20p.m
  Implements a three‑stage strategy to select 20 (PGA, C, α) combinations that are most informative for model calibration.
  Stages:

  1. Boundary exploration (6 points): selects extreme points covering all five PGA levels (0.1g, 0.2g, 0.3g, 0.4g, 0.5g) and the corners of the C‑α space.
  2. Uncertainty sampling (7 points): picks points with the highest predicted model uncertainty, based on the distance to already selected points (the farther, the more uncertain).
  3. Response diversity sampling (7 points): picks points in regions where the model response is expected to be most sensitive (near a sensitive region defined around C = 12000 kN·(s/m)^α and α = 0.5).
     The script ensures that the final set of 20 points has a balanced distribution across the five PGA levels.
     Outputs:
  • Excel file: Calibration_Points_20_yyyymmdd_HHMMSS.xlsx with columns: Point_ID, PGA_g, C_kN_s_m_alpha, Velocity_Exponent_alpha, Selection_Stage.
  • MAT file: Calibration_Points_20_yyyymmdd_HHMMSS.mat containing the same data along with the parameter ranges and selection details.
  • A figure showing the selected points in 3D (PGA, C, α) and the PGA distribution.

• sample_200p.m
  Generates 200 points in the C–α space using Latin Hypercube Sampling (LHS) with the maximin criterion to achieve good space-filling properties. The PGA is fixed at 0.3g (the design earthquake level) for simplicity, but the user can modify the script to vary PGA if needed.
  Workflow:

  1. If the Statistics and Machine Learning Toolbox is available, it uses lhsdesign; otherwise, a manual LHS implementation is used.
  2. Scales the normalized samples to the actual ranges: C ∈ [2000, 25000], α ∈ [0.3, 1.0].
  3. Computes quality metrics: minimum point spacing, correlation between C and α, and marginal uniformity.
  4. Saves the design points in an Excel file LHS_Samples_N200_yyyymmdd_HHMMSS.xlsx with columns Sample_ID, C, α.
  5. Also saves a MAT file with the same data plus the quality metrics.
  6. Produces a 2D scatter plot with marginal histograms to visualize the distribution.

Code/Software Requirements

• MATLAB R2022b or later is required to run all scripts. The following toolboxes are necessary:
  • Optimization Toolbox (for gamultiobj)
  • Statistics and Machine Learning Toolbox (for lhsdesign, pdist, randsample, etc.)
  • Deep Learning Toolbox (for neural network functions such as newff, newgrnn, newrb, sim, mapminmax)
  • Parallel Computing Toolbox (optional, can speed up the genetic algorithm).
• SAP2000 version 10 is required to open and run the finite element model files in their native format (.SDB). However, the model definitions are also provided in .s2k (text) and .xls (Excel) formats:
  • The .s2k files can be viewed and edited with any text editor; they can also be imported into SAP2000 or other software that supports the SAP2000 text format.
  • The .xls files can be opened with Microsoft Excel or open‑source spreadsheet applications (e.g., LibreOffice Calc, Google Sheets) to inspect model parameters.
    To perform parametric analyses from MATLAB using the original SAP2000 models, the OAPI must be enabled, and the .SDB files must be used. Basic knowledge of SAP2000 OAPI is assumed for users who wish to generate new data.
• All custom MATLAB functions are included in the scripts; no external libraries or additional toolboxes are needed beyond those listed.

Usage Instructions

1. Reproduce the M1 surrogate training:
   • Open MATLAB, navigate to folder 2 Neural network model.
   • Run RBFN.m (or BPNN.m/GRNN.m) to train the network. This will generate trained_model1.mat.
   • The script automatically reads M1-DataSet-in.xlsx and performs normalization and training.
2. Generate M2 calibration data:
   • If you have SAP2000 v10, load M2.SDB from folder 1 SAP 2000 FEM model. Use the OAPI interface (a separate MATLAB script is not included; users must write their own or use the provided sampling points to run analyses) to execute parametric runs with the design points generated from sample_20p.m or sample_200p.m.
   • If you do not have SAP2000, you can still inspect the model definition using the provided .s2k or .xls files. To generate new analysis results, you would need to recreate the model in another finite element package that supports the .s2k format or use the exported Excel data as a reference.
   • Collect the results (input variables and output responses) and save them as a MAT file named M2_FEA_results.mat with either:
     • a structure containing fields X (N×7) and Y (N×4), or
     • a matrix of size N×11 where the first 7 columns are inputs and the last 4 are outputs.
   • Place this file in folder 3 Transfered surrogate model.
3. Perform transfer learning:
   • Ensure that trained_model1.mat (from step 1) is present in folder 3 Transfered surrogate model (or copy it there).
   • Run main_transfer_learning_complete.m. This will produce:
     • M2_calibrated_model_complete.mat: the calibrated surrogate model.
     • M2_performance_results.mat: performance metrics comparing the direct M1 model and the calibrated model.
     • M2_calibration_results.png: a scatter plot of predicted vs. true values for the four outputs.
   • The script also displays detailed progress and results in the MATLAB command window.
4. Run multi‑objective optimization:
   • Copy the calibrated model (M2_calibrated_model_complete.mat) to folder 4 Hybrid Surrogate optimization Framework and rename it to trained_model_enhanced.mat (or modify the script to load the correct file).
   • Run main_FVD_optimization.m. The optimization may take several minutes depending on the population size (80) and number of generations (100).
   • All results will be saved in the subfolder optimization_results_enhanced/. Examine the figures and tables to interpret the Pareto front and the recommended design.
5. Generate new sampling points (optional):
   • To create a custom set of 20 calibration points, edit sample_20p.m to modify the PGA levels, parameter ranges, or the random seed, then run the script.
   • To generate a 200-point LHS design, run sample_200p.m. The output can be used for uncertainty quantification or as input to the SAP2000 parametric runs.

Access Information

• DOI: 10.5061/dryad.5mkkwh7k9
• Related publication: Han, Z.; She, D.; Liu, J. A Transfer Learning-Based Hybrid Surrogate Modeling Framework for Efficient Multi-Objective Seismic Design of Long-Span Cable-Stayed Bridges. Buildings 2026, 16, 904. https://doi.org/10.3390/buildings16050904

For questions, issues, or requests for collaboration, please contact the corresponding author at hanzf@hfuu.edu.cn.

How to cite this dataset:
Han, Z.; She, D.; Liu, J. (2026). Data from: A transfer learning-based hybrid surrogate modeling framework for efficient multi-objective seismic design of long-span cable-stayed bridges. Dryad Digital Repository. https://doi.org/10.5061/dryad.5mkkwh7k9