Covariate-Adjusted Functional Data Analysis for SHM

2024-10-07

• Reproduction details and instructions
• Extract bridge data
• Case study 1 - computational results
• Case study 1 - plot results
• Introduction and misc plots
• Simulation study: model training pipe line - computational results
• Simulation study: model training pipe line - plot results
• Simulation study: monitoring scheme run length - computational results
• Simulations monitoring scheme run length - plots
• References

Reproduction details and instructions

The folders contain the following files, which have been used to generate the results and plots of the paper (Wittenberg et al. 2024). For each file an input and output is stated, which describes the required input data and the generated output files. The files are written in the R language and replications can be achived by rendering the qarto “.qmd” files in the R environment.

To run all codes the following R-packages are required:

# Package names
packages <- c("benchmarkme", "dplyr", "forcats", "funData", "ggplot2", "gratia", 
              "lme4", "lubridate", "mgcv", "patchwork", "plotly", "purrr", 
              "refund", "R.matlab", "segmented", "spc", "tidyr", "tidyselect", 
              "xtable") # "reticulate" and "png" are not required.
                        # R package "reticulate" can be used to run Python code in 
                        # R and save the 3 dimensional plots. The R package "png"
                        # can be used to to include png files.          

# Install packages not yet installed
installed_packages <- packages %in% rownames(installed.packages())
if (any(installed_packages == FALSE)) {
  install.packages(packages[!installed_packages])
}

# Packages loading
invisible(lapply(packages, library, character.only = TRUE))

Extract bridge data

The file Extract_KW51_bridge_data_Maes.Lombaerts_2021.qmd downloads and extracts the KW51 data set which is freely available from https://zenodo.org/records/3745914, cf. (Maes and Lombaert 2020), and for information on the bridge compare (Maes and Lombaert 2021).

• Output:
  • data/Dataset_bridge_KW51.RDS (Compiled data set for the KW51 bridge)

Case study 1 - computational results

The file Case_study_1_computational_results_KW51_Mode06.qmd replicates all computations of the KW51 case study in Section 3 of the main paper.

• Input: Dataset_bridge_KW51.RDS (Compiled data set KW51 bridge)
• Output:
  • data/mode06_gam2_fpcaRes.RDS (Basic model eigenfunctions)
  • data/mode06_gam2d.RDS (Basic model refitted)
  • data/mode06_dtaiB2.RDS (Data including eigenfrequencies)
  • data/mode06_gam4d.RDS (Reduced model refitted)
  • data/mode06_dtaiB4.RDS (Data including eigenfrequencies)
  • data/mode06_gam6d.RDS (Additive model refitted)
  • data/mode06_dtaiB6.RDS (Data including eigenfrequencies)
  • data/mode06_gam7_fpcaRes.RDS (Interactions model eigenfunctions)
  • data/mode06_gam7d.RDS (Interactions model refitted)
  • data/mode06_dtaiB7.RDS (Data including eigenfrequencies)
  • Table 1 (R squared results of all four models)

Case study 1 - plot results

The file Case_study_1_plot_results_KW51_Mode06.qmd replicates all KW51 case study related plots in Section 3 of the main paper.

• Input: All saved output results stored in data folder from file Case_study_1_computational_results_KW51_Mode06.qmd
• Output:
  • Figure 4 (Eigenfunctions basic model)
  • Figure 5 (Basic model effects)
  • Figure 6 (Reduced model effects)
  • Figure 7a (Additive model intercept effect)
  • Figure 7b (Additive model covariate effects)
  • Figure 8a (Interaction effect model intercept effect)
  • Figure 8b (Interaction effect model covariate effect)
  • Figure 9 (MEWMA control charts in different setups)

Introduction and misc plots

The file Introduction_and_misc_plots.qmd replicates the introduction profiles and data generation process plots.

• Input: Dataset_bridge_KW51.RDS (Compiled data set KW51 bridge)
• Output:
  • Figure 1 (KW51 data exemplary response, covariate and error profiles)
  • Figure A1 (Artificial data exemplary response, covariate and error profiles)

Simulation study: model training pipe line - computational results

The file Simulation_study_model_training_pipe_line_computational_results.qmd computes 100 runs with J profiles and saves data to data/simulations folder.

• Input: -
• Output:
  • generated data files (estimated basic model and eigenfunctions) in a specified folder

Simulation study: model training pipe line - plot results

The file Simulation_study_model_training_pipe_line_plot_results.qmd plots initial functions, simulated data run profiles and their mean.

• Input:
  • data/simulations/Simulation_study_N300_NAOBS0_SEED42_ML.RDS (Simulated profiles for J=300)
• Output:
  • Figure A2 (Model training pipeline results on simulated profiles)

Simulation study: monitoring scheme run length - computational results

The file Simulations_study_monitoring_scheme_run_length_computational_results.R is an R-script prepared for parallel computing the run-lengths of the MEWMA control charts.

• Input:
  • fpcaResSim_simulation_runlength.RDS (eigenfunctions for artificial data)
  • gam2d_simulation_runlength.RDS (Basic model for artificial data)
  • repeat the script for different lambda settings (0.1, 0.3, 1)
• Output:
  • Run-length files for different MEWMA smoothing parameters

Simulations monitoring scheme run length - plots

The file Simulations_monitoring_scheme_run_length_plots.qmd plots ARL profiles for different MEWMA smooting parameters.

• Input:
  • data/simulations/ (Average Run Length profiles for lambda=0.1,0.3,1)
• Output:
  • Figure A3 (MEWMA charts Average Run Length performance comparison)

References

Maes, K., and G Lombaert. 2020. “Monitoring Railway Bridge KW51 Before, During, and After Retrofitting. V1.0.” https://doi.org/10.5281/zenodo.3745914.

Maes, K., and G. Lombaert. 2021. “Monitoring Railway Bridge KW51 Before, During, and After Retrofitting.” Journal of Bridge Engineering 26 (3): 04721001. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001668.

Wittenberg, Philipp, Lizzie Neumann, Alexander Mendler, and Jan Gertheiss. 2024. “A Functional Data Approach for Structural Health Monitoring.” https://arxiv.org/abs/2408.02106.